What info have we on the capabilities of their ships?
They're fast, really, really, really,
really fucking fast.
They can cross what is effectively the entire galaxy in under a week/month/year depending on your estimates. Either of the three interpretations makes them stupidly fast regardless of which you take really.
That's about it though lol. The ships invading Klendathu have some turrets on their hull, but they're never used for planetary strikes - they instead rely on aerospace fighters to do that work - or to try and intercept large asteroids. So I assume they're probably for vaporising small pieces of space debris that might strike sensitive equipment jutting from the ships hull.
In the animated films, there are some actual warships shown off, as well as space defences. Wiki says they fire lasers, I say they fire some form of charged particle beam, because those are clearly not even close to what a laser looks like.
Their big warships have a few top mounted turrets, and a large battery of prow mounted guns. The small fast attack ships have top mounted turrets. They seem to be unable to hit the broadside of a barn, the damage they do doesn't seem to be particularly impressive either. At one point, the smaller ship takes two direct hits to it's engine struts, from the front battery of the big warship, and it does dick and all to it.
The UFP is going to absolutely molest the Terran Federations warships into submission. Even going by lower end stuff, they outrange them significantly, their guns appear to just be better. They have shields to make every hit except a killing blow largely not relevant, and in exchange could probably pin point reactors, command decks, and weapons control points with sensors, then bore clean through them with phasers/photon torps.
From the showing in the animated films, I'd say something like the
Yeager class could go like 3-1 against Terran ships. From the films only? You could built a fleet of
Danube Class ships and let academy students run fleet battles as a training excercise to wipe out their military.
The biggest danger would probably be if the Terrans government collapsed, their FTL tech got out, and they traded for better ships. Because with their ideology, government and citizenry, they'd be more than happy to gore unaligned alien worlds for resources, slaves, and technology.
EDIT: Okay, so there's a Starship Troopers TTRPG set in the film universe, I was hoping there was information on the warships weapons there that might be enlightening. There is, but not in a way that helps the Terran Federation. But it does explain things.
Pilots - of fucking warships! - need only 20 hours in a simulator to take a pilots exam. Which would probably be why every pilot we see in the films is literally incompetent. The warships we see in the film are also unarmed because they were refitted to be so, as the one we see (Rodger Young) is said in the TTRPG to be a refitted Command and Control vessel. That's a retarded decision to be sure, but justifiable if the rest of the fleet is armed. Their warships according to the book carry 'cannons', which I'll take to mean the above seen particle beam weapons, and fusion tipped nuclear warheads.
Fighters carry a mass of railgun mounted nose guns, HEAT missiles (why? The bugs aren't armoured enough to resist shrapnel, let alone anti-tank weapons.) and can be refitted to replace the HEAT missiles, with dumbfire carpet bombs. The book does mention the skinnies as well - which are maurauder canon but meh - and says that they have around a dozen defence satellites that are able to hold off the entire Federation fleet. Because their energy weapons can literally gut a ship from prow to stern in one shot; and their ships take around a 5-1 ratio of dedicated warships to transport shuttles. So yeah.
Also, it says that the Terran Federation has only 25 colonies, and all are within 11 light years of Earth in a sphere. It also includes something that directly contradicts the films, as it says that the top speed that can be continuously maintained by a warship is 3 parsecs a day. Which is faster than pretty much any other federation ships cruising speed at about warp 9.9, it is also fucky; since warships can be slowed down by realspace gravity disturbances, and dragged out of superluminal speeds by going 'near' (whatever that means in space) solar systems.
I would also like to add this, this is a tactic that the fleet uses to support ground troops:
Rain of Fire: The codename given to Mobile Infantry
troopers capsule dropping from starships in orbit over a
target world, the rain of fire is so abrupt that few enemy
forces have a chance to intercept it or prepare themselves
for the rapid deployment it represents. A rain of fi re
usually covers a wide area in and around a drop zone,
allowing troopers to surround an objective in a very
short amount of time.
If you call for an airstrike, they'll just throw dudes out the fucking airlock at you.
Hilarious.