This is a bit of a hard thing to answer because a lot of the time, the abilities of the ships make them case specific. I have different reasons for picking a radiance than I do a Devastator, for example, but here's the best way to sum in general.
Battleship:
1. Kol
2. Devestator
3. Radiance
This list could be put in any order in my opinion.
The Kol is just a beast, it's a rock, and get it past level 6 and the thing just won't die.
The Devestator is a pretty solid 1 v 1 battleship, and it's still a beast. It's antimatter sucking ability is nice too.
The Radiance is a bit weaker than both of the others, but there's a trade-off here. The Radiance get's cleansing brilliance, an absolutely kick ass level six ability that when combined with malice is lethal.
Winner: Kol
Carrier:
1. Halcyon
2. Sova
3. The Vasari One
The Advent Halcyon gives that beautiful aura which is great as a second or third cap supporting ability.
The Sova has the embargo. Useful for rushing and not a bad supporting cap for a larger fleet.
The Vasari Carrier is frankly forgettable. The repair cloud is eh. The level 6 ability is eh. I personally don't like the thing, but some people do.
Winner: Halcyon
Colonizer:
1. Mothership, Akkan, Evacuator ( I love 'em all )
The colonizing ability for a cap in early game is invaluable, and that makes this the best 1st cap IMO regardless of race, but outside of the colonize ability, the Mothership wins hands down. Malice, shield regeneration, and an ok level 6 ability are just crazy. Not to mention it makes planet upgrades cheaper.
The Evacuator has the nanite bomb thingy, and the slow down bomb thingy, but what I love about this ship is it's a seige engine once you get to level 6.
The Akkan's level 6 armistice is a beauty. Once you get to level 6, you'll never lose this cap. It's also nice for when you have to retreat and you don't want your enemy picking apart your retreating fleet.
Each colonizing cap just kicks SO much ass.
Winner: Mothership, Evacuator, Akkan
Support:
1. Dunov
2. The Advent One
3. The Vasari One
None of these are really bad imo, but I think the Dunov is underappreciated. The level 6 ability cuts antimatter costs 300%. Mix that with an allied Advent fleet, and you're practically guaranteed a win. It also has an antimatter takeaway ability, and a shield regenerator that will save your caps in a pinch.
The Advent one, the Rapture I think, has Vertigo. Very nice support ability, but it's level 6 doesn't turn the tide of a battle, and the increased damage aura for fighters has too small a range.
The Vasari one has it's uses. The phase-out hull makes it impossible to kill and it's level six can be tactically useful, but I still don't like this ship.
Winner: Dunov
Seige:
1. Marza
2. The Vasari One
3. The Advent One
This one hands down is the Marza. Are you kidding me? This thing levels planets. The nuke ability is somewhat useful, and the damage bonus is nice, but the seige ability is all this thing needs. The level six is kinda useful against an advent fleet that is using guardians.
The Vasari one does good Damage per second, but that's about it, even with it's supporting ability. The phase missle swarm is weak, but still, I like the ship.
The Advent one has very limited use until level 6 as a seige engine like the others. It's just not a seige engine. It has some good support abilites, but I don't like this thing. I rarelyl pick it.
Winner: Marza
