There is no always better.
A lot of the benefits in land warfare (light means more rounds) are discussed elsewhere, so I'll address effectiveness and role.
I think the more important question is what are the weapons built to accomplish.
A light projectile has less mass so you can accelerate it fast and you can also decelerate it fast, so your effective range is likely pretty small even if your maximum range is very long.
You'll have three modes with a fast, light projectile:
overpenetration: hit the target with a needle going Mach 3 - punches through and deposits basically no energy
underpenetration: hit the target with a needle thrown by a 12 year old - no energy left after flight drag
effective: hits the target with enough kinetic energy to be lethal - due to low mass, crumbles and collapses on impact, imparting all energy to the target
If these are battle rifle-type weapons, I'd presume they're designed to be effective against those who use them. In that case, I'd presume their users are insect-like. Very fast, stealthy when they want to be, can change direction quickly and have little to no muscle, but potentially carapace. In this case their doctrine would likely be to spread out and ambush using a triangulation of crossfire to fill the target area with rapid, effective fires at medium to close range and aiming for soft parts (head, eyes) with point fire. If the enemy closes the natural overpenetration of the weapons makes them more likely to pierce carapace, so lay down heavy grazing fires at center of mass targets. Their engagements would likely be mostly silence followed by a massive, violent scrum. They'd focus a lot on movement, tracking and situational awareness. Maneuver and unit cohesion would be key as well as furious and uncompromising personal combat. There likely wouldn't be snipers or designated marksmen. Being alone makes you prey. Even if you knock down one, there are fifteen behind you.
On the other hand a heavy projectile has lots of mass, so even though you can't accelerate it fast you also can't decelerate it fast, so your effective range is likely quite long even if your maximum range is shorter.
You'll have the same three modes with a slower, heavy projectile of over- and underpenetration, as well as an effective range, however your effective band will take up more of the maximum range. Overpenetration is also likely to be lethal. Shooting a needle through a target is not fun, but likely not lethal. Driving a softball through a target is likely going to be lethal, even if most of the energy stays with the projectile.
If these are battle rifle-type weapons, I'd presume they're designed to be effective against those who use them. In that case, I'd presume their users are large mammalians or reptiles on the order of bear, rhinos, elk, elephants or dinosaurs. Very large, heavy skeleton apex predators or omnivores with fat and muscle layers, likely with dense hide, fur or armored plates. They're likely fairly ponderous in regular life, careful and calculating. In this case their doctrine likely is to scout, locate and strike asymmetrically out of range or from an unexpected direction with precision and then, failing that, to fire for effect, break contact and reset. Continuing to fight after revealing your location and tactical situation is foolhardy because once an enemy knows where you are, you are at a disadvantage and little more than an amusing target. Their engagements would likely be sniper battles. There would be occasional shots. Superior marksmanship, fieldcraft, hunting acumen and the ability to out think and read your enemy would be key. Units would be more like federated hunting parties with blinds, bluffs, ambushes and lures. Battles would play out like a football game over a wider area as each group jockeys for position while protecting their own assets. Being hit anywhere would likely be a fairly high trauma wound and if not fatal, would slow you down and make it harder to think, making you an easier target and starting the death spiral. Shrewedness, calculating precision and personal capability would be fundamental. A weapon is only as useful as its operator.
Whoever would win is whoever could adapt the fastest. Both could win.
The long-range effectiveness of the big bores would catch the light shots off guard. They'd need only a glance and a good guess to rain down deadly fires. The light shots need a way to get in close.
The group assault tactics of the light shots would catch the big bores off guard. They'd only need a few in penetration range, and then a big bore wouldn't have time to get to an advantageous position and sight in. The big bores need a standoff mechanism or a fast response.
The big bores would need to rely on their hunting acumen and inventiveness.
If they pivoted on the light shots needing to get in close they could establish a system of interlocking fields of fire so that no approach is safe. All they'd have to do then is sit and wait for their quarry to appear, which they're more than happy to do.
They could also easily convert a large bore weapon to a shotgun and start carrying sidearms to repel close-in assault. An increase in rate of fire and higher capacity magazines as well as patrolling in pairs would blunt the effectiveness of light shot ambushes.
They could prepare static defenses like mines. If the light shots can't get close, they can't be effective.
The light shots would need to rely on their numbers, speed, stealth and inquisitiveness.
If they realized the big bores are only effective at range, they'd need to either close fast or start close. Deploying sleeper units in random places to wait for big bores and attack opportunistically, or use their superior mobility (digging, flying, climbing) to come at big bores from many directions at once and directions they don't expect could allow enough to get in range to be effective.
The goal would be to splinter a hunting party in to smaller groups or individuals so they couldn't overwatch each other or respond to contact. They'd then be easy pickings to swoop down on. Randomized tactics would keep the big bores guessing. The assault, once started, should be constant to keep the big bores from taking a breath to plan.
It would not be hard for the light shots to convert captured big bore weapons in to crew-served weapons. If they can pin down a big bore with long range fire, they can easily swoop in and nail it.
As far as exosuits, you may want to lean in to that and have the big bores be human-sized, but trying to fight against dinosaur-sized predators. You may also want to dial it down and have exosuits be more like upscaled smartgun assist armatures the colonial marines used in "Aliens!".
In general, start with why. Why do they have light and fast? It works. Why does it work? It is effective against most of the things they want to shoot at. Why? Light and fast is pretty good at hitting light and fast targets close in. Vice versa for the opposite. You can see how I worked forward from there. What is small and light and effective close in? Insects. Based on their physical stature you can extrapolate tactics and in part the warrior culture, which would effect strategy and ethos.