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

I should clarify, I said the Mothership wins hands down, but I love all three so much, I don't have the heart to put the Akkan and Evacuator at 2 and 3.

Couldn't agree more. The more I use the Dunov, the more I appreciate it. When you're facing a Vasari opponent who's got a load of Subverters and Overseers, it's nice to just remove their anti matter with the area effect EMP weapon the Dunov gets. For TEC, running two Dunovs together works good, as does Kol / Dunov and, if you like 3 caps, Kol, Dunov, and Sova with interceptors for bomber defense and LRF hunting.

EMP Charge is particularly effective against Advent and Vasari, since a lot of their power is in either support cruisers or special abilities.