TL;DR: tractor spacecraft with tensile structure are great for everything that doesn't require many frequent changes of direction or acceleration.
Shuttles and warships probably wouldn't use that design, but for everything else there's a reasonable chance that the benefits outweigh the downsides.
In my ever-so-humble opinion, the primary benefit of tractor-configuration spacecraft is reduction in radiation exposure.
To my knowledge, almost all tractor-configuration rocket designs of the last 60-70 years use a tensile structure... there's no rigid spine. (Note that some people still think that a rigid rocket in tractor configuration is somehow more stable, which isn't the case. Goddard's first liquid-fuelled rocket used that design, and he went on to demonstrate it was no better than a pusher-rocket in terms of directional stability).
There are a few immediately obvious real-world benefits to using a tensile structure.
You can protect yourself from radiation by putting enough mass between you and the source, or you can move the source far enough away from you that the inverse-square law protects you from the worst of it. Some early work on this notion can be found in the form of the Convair Helios which used a nuclear thermal second stage. The San Diego Air and Space Museum has a nice collection of images online, including these wonderful illustrations by John Sentovic for the original proposal in 1959 (which I'd like to find a copy of, but can't).
The distancing was far too short of course... I won't go into details here, but a 300m separation from a gigawatt nuclear thruster would have been a bit spicy for the payload, which would have included humans (at least at takeoff).
Here's another illustration from the same series:
This shows how the nuclear engine could lower the crew module to the ground, then move laterally to land itself, maintaining separation at all times. This is perhaps a predecessor to the Mars Science Laboratory's "skycrane" Entry-Descent-Landing system.
Charles Pellegrino, author of Flying to Valhalla and consultant for the ISV Venture Star design of Avatar fame, thought carefully about the design of a fast interplanetary or interstellar rocket design, which he named Valkyrie:
Put the engine up front and carry the crew compartment ten kilometers behind the engine, on the end of a tether. Let the engine pull the ship along, much like a motorboat pulling a water skier, and let the distance between the gamma ray source and the crew compartment, as the rays stream out in every direction, provide part of the gamma ray protection - with almost no weight penalty at all. We can easily direct the pion/muon thrust around the tether and its supporting structures, and we can strap a tiny block of (let's say) tungsten to the tether, about one hundred meters behind the engine. Gamma rays are attenuated by a factor of ten for every two centimeters of tungsten they pass through. Therefore, a block of tungsten twenty centimeters deep will reduce the gamma dose to anything behind it by a factor of ten to the tenth power (1010). An important shielding advantage provided by a ten-kilometer-long tether is that, by locating the tungsten shield one hundred times closer to the engine than the crew, the diameter of the shield need be only one-hundredth the diameter of the gamma ray shadow you want to cast over and around the crew compartment. The weight of the shielding system then becomes trivial.
There's considerably more information about his Valkyrie spacecraft design on his website, but do note that this isn't a scientific paper. I'm not aware of more serious studies on this style of rocket. For non-generational starships, beamed propulsion systems are more desirable than self-propelled systems, which might be part of the reason. Further discussion on this subject probably belongs in a separate question though.
It is pretty well known that you can use centrifugal forces to provide artificial gravity for spacecraft. To provide sufficient centrifugal force, you can do two things: spin your centrifuge fast, or extend the radius of your centrifuge. There are physiological limits to the "just speed it up", because the difference in centrifugal forces across a short-radius centrifuge can be quite disorienting and coriolis effects make working in such an environment challenging... there's plenty of research on this, such as Artificial gravity space station physiological effects and design criteria from 1971.
The Gemini Xi Artificial Gravity Experiment was almost certainly the first actual use of centrifugal artificial gravity in space, generating a fierce 0.15 milligees of acceleration, but if you really wanted to use this design for artificial gravity there's no reason to limit yourself.
Martin Marietta wrote Manned Mars System Study for NASA in the late 80s, and one part of the study included looking at artificial gravity provision for astronauts on an Earth-Mars transit.
The use of long tethers allowed for low rotation rates (~2rpm) but high artificial gravity (as much as 1 gee!). Regular pusher spacecraft could do this as well, but they'd have to carry the tether equipment in addition to their normal structure making it additional weight. Tractor spacecraft could get it "for free", so to speak.
It should be obvious that you can't use this style of artificial gravity whilst your spacecraft is under thrust, but for in-system travel this should not present a problem. Everyone always goes on about constant-thrust brachistochrone trajectories, but boost-coast-brake trajectories can be almost as fast and need much less implausibly overpowered rocket motors (but that's a subject for a different question).
High-speed (eg. >.2c) starships would probably not use this mechanism at all, because it would expose too much of the spacecraft to high-speed debris and particle radiation from ahead... read more gristly details in Radiation Hazard of Relativistic Interstellar Flight. Different artificial gravity designs are required for those kinds of flight, with everything tucked behind a substantial forward shielding system. Generational spacecraft with more modest speeds and shielding requirements could work just fine, though.
Novel propulsion systems
Lightsails more or less require you to have a tractor-configuration spacecraft. Laser driven lightsails are potentially quite useful and sensible designs for both in-system and interstellar travel, and remove all that tedious mucking about with the rocket equation. Lightsail sizes need to be big (I won't go into detail about how big, but to give you decent accelerations or to push you to another star in a reasonable timescale they need to be kilometers across) and making very lightweight rigid structures that could be use for pushing is more or less impractical.
High speed and high acceleration lightsails need to be curved to reduce tensile stresses in the sail fabric causing tears. Making a nice curved sail with the payload tethered "behind" it is a fairly natural and simple design, in theory.
Lightsails aren't the only thing you can do though. A paper for the British Interplanetary Society in the 90s gave us the Medusa, an Orion-like nuclear pulse propulsion system that used a curved sail-like system that the author referred to as a spinnaker to catch the products of a nuclear explosion:
(the original paper, Medusa – Nuclear Explosive Propulsion For Interplanetary Travel, is currently paywalled, and I have no free sources for you)
The Medusa propulsion cycle is conceptually similar to Orion, detonating the nuclear propulsion unit, catching the blast in a canopy (instead of a pusher plate). The canopy is blasted away from the spacecraft, unspooling the tether as it goes. The ship then reels itself back in along the tether. This reeling-in stroke can be made much, much longer than the Orion's short stroke, providing an extended period of artificial gravity as the spacecraft is accelerated towards the sail. The shock loading is much less because the stroke is longer, reducing mechanical loads on the spacecraft and reducing the weight of the shock-absorbing system. The great length of the tether also allows the inverse-square law to provide additional protection from radiation that the much short Orion ships cannot enjoy, requiring them to carry much more shielding.
The principle downside is that you have to care about where the exhaust jet goes. With a pusher-configuration, so long as you're in deep space then you can fart out as much toxic and intensely radioactive death gas as you like and you'll probably be OK (so long as you're suitably shielded). With a tractor configuration, you need to make sure that you are the exhaust jet doesn't impinge on any other part of the spacecraft, and that any radiation emitted by the jet (including thermal radiation, not just short-wavelength EM and fast particle radiation) doesn't threaten the safety of the spacecraft.
The Convair Helios just had a single motor and placed the crew module sufficiently far away that the exhaust jet was expected not to be a threat, but more powerful engines can't really make that assumption. If nothing else, the tethers themselves are at risk of damage... look at the Helios image above and you can see that the tethers are mounted on booms that hold them away from the rocket's body to prevent them being melted through by the exhaust.
The Venture Star design angles the two big nuclear rockets away from the spacecraft to keep the jets away from everything. Project Rho says they're out by 3 degrees, by I can't find where he got that information from (the Pandorapedia says nothing about the angles, for example, but maybe there are better sources). I'm assuming he just put a protractor up to the diagrams and artwork, and that's good enough.
You can work out the thrust lost from angled jets by taking the cosine of the angle to get the vertical component. The cosine of 3°, for example, is ~0.9986, meaning that 0.14% of the thrust is wasted. That's not a trivial amount of delta-V, but it also isn't necessarily a mission-ending waste.
If you don't use rockets then this really isn't much of a problem, of course.
A much lesser downside might be manoeuvrability. The tractor design means your spacecraft doesn't need to have a stiff spinal structure, and that's great when you're just going in a straight line, pulling from the front, but this can present some difficulties when you need to slow down or turn and maintain tension in the structure. If you're just flying from A-to-B this probably isn't a big deal unless you have a lot of space-traffic-control manoeuvring to do, but in that case you can just use smaller pusher-configuration shuttles to fly stuff into airspace where more turning and changes of acceleration are needed. For interstellar travel, the whole "not being able to turn on the spot" thing isn't a problem at all, because turning around when you're travelling at relativistic speeds is a good way to get irradiated to death. Note that this was something that the ISV Venture Star design got very wrong. Flipover at .7c kills everyone. That's why Pellegrino's Valkyrie designs either used a boost engine and a brake engine (one at each end) or in the event of an emergency, reconfigured the ship to thread the crew module through the (inactive) booster engine to move it to the back of the spacecraft for braking without flipping the whole ship over and compromising its radiation shielding.
Your additional questions:
How will the size of the ship affect such and the power needed to propel such a craft?
If your tractor system is lighter than its pusher counterpart, then you get more cargo or more fuel and reaction mass or more shielding "for free".
The size of the ship is almost irrelevant, although it will be much easier to make multi-kilometer-long tensile spacecraft, than rigid ones.
Like, Can something as big as a Generation Ship utilize a tractor-configuration and ships of such proportions?
Probably not, but not because of the tractor configuration per se but because of the fact that you probably can't reasonably keep a propulsion system running across generational timescales. Your rockets will have run out of fuel, your laser emitter at your home star might not be maintained or simply might be unable to focus at such a distance.
MatthieuM mentioned solar sails driven by starlight pressure alone, but even these will only provide useful thrust within the launching starsystem and all the useful acceleration will be over long before they reach their equivalent of the heliopause and the sail should be packed away safely to protect it from damage, ready for use as a solar parachute to decelerate at the destination system.
Most of a generation ship's flight will be cruising without thrust, and so the configuration is kinda meaningless. The boost and brake phases could use a tractor-configuration, conceivably.