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At a crucial point in the development of human civilization, there is a split in the timeline: one where FTL travel is facilitated by jump-drives/wormholes, and another with superluminal speeds (Star Trek's warp drive).
How differently would these societies develop, assuming the energy-consumption per lightyear were the same for both?
Since these technologies are both fictional, you can make up any rules you want. However, I think that the laws of economics, as applied to moving around on Earth, will generalize. (Also the laws of force and conflict).
So, the key parameters:
Speed. It seems reasonable that, in the same starship, it takes twice as long to go 200 light-years superluminally as it does 100. It also seems reasonable that with a jump drive, it takes a constant set-up time to get to and from spaceports to jump-points, and the jump is instantaneous. So time per journey is constant, up to the maximum range. Sensible times could range from hours to years per journey. ("Teleportation" with effective zero set-up time would be a military nightmare and probably leads to first-strike armageddon).
Different speeds? Can a starship make a quicker journey at added cost? Or is there effectively one and only one speed? Boats have a very limited ability to go faster.
Cost. What does it cost per kilogramme of freight? And is distance, within range limit, a significant price factor or not?
Range. What is the range limit, before a starship has to stop to be refuelled or overhauled? (Also, is "Earth" the only place such an overhaul is possible, either because of its complexity or for political reasons? )
Scale. How small is the smallest possible starship? How large is the largest? Here on earth, there is a maximum size for an aircraft set by the materials-science impossibility of making a rigid wing much wider than that on an Airbus 380 or large military transport. (Smallest is inches, or millimeters using related technologies).
Communications. Is there a means of superluminal communication other than sending packets on a starship? If there is, what does it cost per bit transmitted?
Predictability. Consider steamships versus sailships. A steamship's journey time is fairly predictable, only the very worst weather will slow it down. A sailship's journey time is not nearly so predictable.
Safety. Is interstellar travel as safe as today's air travel? Or as dangerous as that of an early settler to the colonies that became the USA? If significantly dangerous, does that depend on a human crew's skill? Or is it a matter of pure, ramdom luck?
Detectability. (Military implications). Do starships betray their transit by creating detectable "wakes"? If so can anything intercept them in transit, or immediately on emergence from transit?
Note: depending on how you set these parameters, it's quite possible to have a universe where jump and superluminal drives co-exist. We still have ships here on Earth, despite aircraft. We still have trains, despite trucks.
When you say "jump drives/wormholes", I'll assume you mean "can jump from any point". Fixed stargates have quite different implications, because then the FTL system isn't part of the ship, and can be militarily threatened independently of any ship.
By your reference to Star Trek, I'll assume that combat is possible at warp speeds. I'll assume that jump drives do not allow this. In some SF universes, it is possible to detect something about a ship as it jumps that gives information on its destination. You have no indication whether this is possible in your universe. If it is, jumping allows you to escape an immediate battle, but not long-term. If jump drives cannot be tracked, then it will be impossible to force combat except around fixed locations (planets and space stations).
Jump drives, particularly untraceable ones, make smuggling easy but piracy almost impossible. Warp ships, whereas, can be intercepted and thus pirated (only by other warp ships, though).
Given that energy costs are the same, warp civilizations will be at a great military disadvantage compared to jump civilizations. However, I expect that space between star systems will be largely claimed by warp civilizations (not that they will be able to control transit by jump ships).
I'm starting with military differences because these will define many of the economic differences by defining what resources it is possible to control.
The other major difference requires information you have not provided. I expect that different methods of FTL travel correspond to different methods of FTL communication.
I'm making the following simplifying assumptions:
OK, let's look at the relevant characteristics of the two transport modes:
Jumping (wormholes, jump ports, stargates etc):
This will essentially lead to the galactic economy concentrating around the jump ports. Any significant distance from the next jump point will be hard to reach, as only conventional travel is available to go there. Since also conventional travel is needed to get to a new location and build a new jump port there, the civilisation will spread relatively slowly around the galaxy, however as soon as a new jump port has been established, the corresponding region will be quick to reach, and therefore there will be extended trade between the different colonization centers. However the limited capacity will increase the price of jumping, so trade between different "settlements" will be restricted to high-value goods, or goods that you cannot get at one of the places (which automatically get high-value goods at those places).
A lot of planning will go into where to build new jump ports, as the initial investment is high (a long conventional journey to the destination). This means that probably only few companies are in charge of the jump port network, or maybe it is even operated by the government.
FTL speed (Warp drives):
The faster travel speed will allow to colonize the galaxy much faster; however the fact that travel time depends on the distance means that trade will be predominantly between relatively near places. The colonization will occur much more uniformly, since every point at the same distance is equally easily reached. Moreover, if you have an FTL ship, you're free to go wherever you want; you don't need to wait for someone building infrastructure at the destination.
Unless FTL ships are very expensive, there will be likely many corporations operating them, and possibly even some rich private persons; also, there are likely many companies building such ships.
A combination of both:
The optimal situation would be a combination of both modes of travel. Then very large distances could be covered by a network of jump ports, but colonization is not limited to the immediate surrounding of those jump ports, but can use the FTL space ships to reach a larger distance from the jump port in reasonable time.
Depends on if time dilation is an issue. A few moments in "real space" doesn't have to take the same time on board a superluminal craft- if for instance, the time taken on board is in order of a few months, whilst the actual time taken is moments, you have a significant supply issue, as well as a higher rate of aging on board. Equally, however, a craft which is approaching at superluminal speeds will have far longer to react, plan and organise their actions when they make landfall.
The delay in travel would mean that the two societies could potentially develop quite differently. In the case of the superluminal travellers, information would be far more important to their ship masters - as they would be able to process far more in transit. They can work for months on information and make better decisions based on what's available. This has obvious advantages in research and development, military strategy, economic and business planning... anything where time is useful.
The "jumper" society would not have these advantages available to them and therefore could potentially loose out to the superluminals in all sorts of areas.
Dependant on how long this goes forwards, however, the superluminals may then be less capable of making decisions speedily, preferring to think things over, leaving them at a disadvantage in "real" space and "real" time.
How differently would these societies develop, assuming the energy-consumption per lightyear were the same for both?
Assuming that there's no FTL communication faster than the mode of transport and assuming that the jumps are instantaneous:
The jump-drives/wormholes civilization could support a civilisation-wide computer network like the internet. Whatever the range of the jump drives or wormholes you place nodes along the paths between major outposts with either wormholes linking them or little ships jumping back and forth. You send a message to the far side of the empire and a few hundred milliseconds later you get the reply. They're going to be able to coordinate better, they're going to be able to trade better.
In your superluminal civ news can only travel as fast as the ships that carry it.
This would have a huge economic effect. In the former you can have almost real-time markets across the entire empire while the latter is going to look a lot more like the world during the age of sail.
A lot of things of course depend on the rules you set for FTL. Can you open up a wormhole inside an enemy ship or any other arbitrary point. Do FTL drives have a minimum size etc.
That question reminded me of the Perry Rhodan stuff I liked when I was younger.
The guys there developed from Jumping to FTL-Speeds, because the first one did have the drawback to render any biological being at the jumping ship dizzy for a couple of moments after performing the jump. Further they created some kind of recognizable shock-wave that was utilized by enemies to detect where a ship emerged from such a jump. That shock-wave could go up to Eleven, so when a compound of ships used this, the devices to detect this did go boom. But... jumps done in that way where pretty fast if I recall correctly - like a stargate "just some split seconds and you emerge lightyears away"
The FTL variant was way slower, adjustable in speed and kept the crew awake while they did the travel. Further, this enabled them to play around with their hyperdrive. Nope, wasn't the Star-Trek way of traveling, they bypassed the real continuum by tunneling through some kind of hyperspace. But at least, their reentries where way more stealthy.
So when you ask for either one or another, why not clash two civilizations that utilize one of them, so you may approach this the author-way.
But if you need a decision you may need to determine how both of them may work. While at the moment they are sci-fi, in your universe they are proven techniques. Well, one of them.
Both decisions would be qual, but will have a big impact at warfare, trade and a smaller one at society. If your ftl-travel causes head-ache, there will be less civil travel I think; or all have to jump into hibernate-boxes before doing so. If it causes a shock upon reaching your destination, you will see restrictions enforced by local authorities to prevent damage of any form. If your travel is stealthy at the other hand you will encounter a flourishing piracy and a more civilian space travel, because it may become as easy as driving.
Conclusion?
So... the type of travel would have a lesser impact than the effects of that travel. When its uncomfortable, logistic tasks would be performed by drones and things that don't suffer from ftl-travel, but when its as smooth as visible in much movies, you will see a lively civilian space-economy driven by human pilots. And freelancers. Imagine you could go everywhere with your spaceship. Do whatever you like to. Settle down at a empty moon and creating a new nation of one? No problem.
Anyway, this form of society would be prone to Darwinian selection, so you will end up with a civilization of great space-truckers.
Addendum 1
More Output requested. Lets make differences between two and two options for simplicity:
Jump-Drive Will pass over long distances instantly, but need time to charge. You can appear where you aim at, and it would be hard to to refuse you this ability in a military way. But maybe the reappearance is a very... vivid action in terms of signal-emitting, that scale with the size of the object incoming. Imagine, this technique would not be very precise in terms of its target-area. so you have to launch yourself some million kilometers away from your target and have to travel sub-light over there. Now imagine this-day cargo-ships would randomly appear somewhere in the ocean 10km from the shore. That would be a dangerous mess, so travel would be aiming above the planets plane and use classic means to reach your final destination. Besides this, maintain a military formation with this circumstances would be a nightmare, so dropping out way ahead your target and take time to reformat yourself would be a common thing. But only IF you have this little random thing.
FTL-Flight Will go from A to B using some kind of actual flight. You may need to pop out this flight to aim for your target again, but if you can adjust you speed down to barely-faster-than-light you could approach pretty well. If you can even observe what happens outside your ship, you could approach planets very carefully. Okay... with the double speed of light. Cut this ;) Another thing is, that you may not create such a burst of rays when stopping your travel. At the very end, you could do a airport like schedule at your space-ports, assigning flight vectors to different ships, when you can be sure of their flight-paths. Doing a military formation would be more easy too, plus you could do shortrange-flights to avoid weapons. Otherwise, you will face weapons that can do this too...
and
smooth travel means that biological beings does not feel uncomfortable in any way when performing such travels. Then space-faring would be a big adventure everyone brave and wealthy enough could participate at. Like said before, this would remove many stupid pilots early on from your universe. At the other side civilian adventures would rise. Jump in your space-yacht and fly off to a unmapped system, maybe finding exotic materials you could claim. Whole companies would employ people to do this. But as a government you would lose the ability to keep control of what your less lawful citizens are doing out there. Get a flight-plan with stop-and-orientate-stops of a ore-freighter and perform a space-piracy act... no one could hinder you. I mean, this days governments fail to prevent all crime at their very 2d countries, so how they should keep order in an endless space in three dimensions? Secret hideouts would pop up at every asteroid usable.
hard travel means that biological beings (and maybe dead structures too) do suffer in varying degrees from travel. No one would do this for fun. If you have a hibernate-chamber to counter this, you need heavy support of a computer to get the ship out of trouble while you wake up again. Even more, why employ human pilots when all they do is sleep? I think under such circumstances all mundane tasks would be done by AI-Systems, and humans will be deployed where more decision making is requested, like exploring new planets in close details. And when traveling from one system to another, you would hop in something that like a big sleeping-wagon. Hmmm... fifth element did this, if I remember correctly. But they never said why this was done (the bad guy was able to ftl without sleep-chambering). Anyway, when it hurts, people would avoid this. When no single unit civil ships do crowd the universe, the government would have a much more easy task to keep order.
So, now feel free to combine them as you like. And think about other ways. When you need a kick-start for your brain, look into the "Sword of the stars" universe, where they do use a whole... five different types of ftl-travel. Railroading at gravity-lines, short-distance-teleporting, classic warp, star-gating from system to system and sling the gravity anomaly your fleet creates through space. But for gaming purposes, they are pretty similar otherwise.
I'm going to narrow this down to handle a single element about how they get from point A to point B: traveling through space vs not. How long it takes to get there, convenience and the energies involved are all the same. The only difference is the FTL drive has to deal with all the stuff between point A and point B and the jump drive doesn't.
You can come up with any explanation you want why the jump drive takes time: BSG style "warming up", Star Wars/B5 "hyperspace", whatever. I'm just reducing this to one variable, because it's a big one.
Dust shields
At orbital speeds, a fleck of paint becomes a deadly bullet ready to tear through a spacecraft. At superluminal speeds... equations for calculating kinetic energy from velocity break down, but let's just say you don't want to hit anything. This includes the dust in the interstellar medium.
To deal with this problem the FTL society would have to develop powerful shielding. This could be as low tech as ablative armor, or some sort of sci-fi repulsive energy shield. Jump drive society would not need this tech. This is overwhelmingly the biggest difference between the two drives.
Very good route maps / FTL sensors
No matter how much shielding you had, you don't want to smack into a brown dwarf or rogue planet. The FTL ship needs very good maps, or sensors which can also operate at FTL (no use finding out about an obstacle after you've already hit it). Preferably both.
A jump drive needs neither. They just need to find a nice, clear spot to jump to.
Gravitational navigation hazards
Obviously the FTL drive will have to go around massive objects like stars, but there are some objects out there so large they noticeably curve space-time for light years around them. FTL ships will probably want to steer clear of them. Fortunately this is just a detour, and they are very easy to spot.
Jump drives can just skip over them.
Other navigational hazards
No matter what it is, the FTL drive has to go around or through it, the jump drive can go around it. This might include galactic centers or supernova remnants.
Jump drives sound pretty good, right? There's a problem...
The Jump Drive Cold War
Assuming there are FTL sensors, an FTL ship can be seen coming and prepared for conventionally. An enemy fleet with jump drives is just there, probably where you least want it to be. Even more terrifying is the prospect of the jumping a bomb to whatever target you like.
The jump drive society would have to develop a way to interdict jump drives, or prevent them from jumping into certain areas. What if they couldn't? The jump drive society would be one of paranoia, at any moment you can be attacked with overwhelming force. Militarily, this is much like the situation in the Cold War. Your options are containment, point-defense, first-strike, and retaliatory-strike.
Containment strategy tries to avoid anyone but you having jump drive technology in the first place. The technology would remain expensive and strictly controlled. This would hamper commercialization of jump drives, like how we don't use micro-fission reactors today. Of course, containment would eventually fail in which case you could act militarily to destroy their jump drive production facilities.
Once your enemy has established near-parity of jump weapons, you could risk a first strike to destroy their jump fleet before they have a chance to use it. In response the enemy might hide a portion of their jump weapons to use in retaliation. Of course, you'd do the same. Such a society might develop a political stance similar to Mutual Assured Destruction (MAD) of the Cold War with jump fleets on continuous alert to retaliate to a first strike. Jumping anything but a precision bomb would be considered morally reprehensible.
Eventually one side would try to develop sufficient point-defenses to think they can stop a retaliatory strike with acceptable casualties. At this point they'd either attack before the other guy does, or de-escalate the whole thing as we did. Even with disarmament, there will always be the specter of a rogue entity building a jump drive weapon limiting its commercial deployment.
