This is mostly from multiplayer point of view but mp also speaks volumes about cap balance. Caps get very little use beyond the first one you get for free. Partly because a lvl 1 cap just isn't cost effective compared to frigates or cruisers but also because multiple caps nerf eachother by sharing XP. Generally it's better to have one lvl 6 cap + more fleet than 2 lvl 3 caps.
First I would like to suggest a smaller XP penalty for using multiple capitals in one fleet - a new 20% XP penalty for each cap beyond the first. Caps would get XP as follows:
2 caps 80% XP
3 caps 64% XP
4 caps 51% XP
5 caps 41% XP
6 caps 33% XP etc..
Now onto individual cap ships. Comments most welcome, Vasari especially.
Marza Dreadnought - Best TEC capship because of far superior DPS to everything and Missile Barrage being by far the most powerful ability in the game. Destroys fleets like no other cap and planets on the side. I'd suggest a target cap for Missile Barrage.
Akkan Battlecruiser - Being weaker than Advent and Vasari colonizers make it a less appealing choice. Giving a free extractor with lvl 1 colonize would probably be a good thing for the Akkan. Ion bolt could last a little longer.
Kol Battleship - Abilities are fine, would probably get picked if DPS was closer to Marza, frontal especially. The four frontal laser beams have less DPS than a cobalt. It looks powerful but really isn't as the DPS spreads out so much.
Sova Carrier - Don't see these anymore. Haven't tried them.
Dunov Battlecruiser - useful support cap, all good abilities.
Jarrasul Evacuator - Almost the only Vasari cap ever seen online. Nano Disassembler and Drain Planet are two extremely powerful abilities that would be good selling points of any battleship or siege cap. Put them on a colonizer and you get three caps in one.
Skirantra Carrier - don't see them used. Seemed very fragile last time I tried one.
Kortul Devastator - ??
Vulkoras Desolator - Good at siege but not needed as lvl 6 Evacuator does it better. Disintegration is also inferior to the Egg's Nano Disassembler in spite of being a lvl 6 ability, the reason being high cost, long cooldown and damage being mitigated by shields. The Evacuator's similar but superior abilities make this ship obsolete. Phase Missile Swarm has been reported to not actually shoot phase missiles.
Antorak Marauder - ??
Revelation Battlecruiser - Really weak survivability. Gets shamefully owned by neutral militia in the beginning. Reverie and Clairvoyance are good abilities but the other two aren't. Has someone ever even used Guidance? Provoke Hysteria isn't the ultimate planet killer in spite of being a lvl 6 siege ability. Sure a lvl 6 Revelation can quickly hurt a maxed out planet but it can't finish planets quickly enough, even the small ones, or leave a lasting penalty on the colony that would make a difference. And it looks like a weird shoe.
Rapture Battlecruiser - Vengeance should apply pre-mitigation to be useful against focus firing which is it's only use really. Vengeance should also retaliate damage from abilities such as Nano Disassembler. Low DPS output and not very durable.
Radiance Battleship - Animosity has been reported to be bugged - you can override the force attacking condition by issuing another command. It should force fleeing ships to turn around and attack. Cleansing Brilliance is rather lackluster by itself without the old overpowered Malice. It's difficult to get off from an optimal firing angle and once you do it's nothing special. It should have shorter cooldown or do more damage. Like the Kol some more frontal DPS wouldn't hurt this battleship.
Progenitor Mothership - Good colonizer and fleet supporter. Malice doesn't get much use over Shield Restore anymore though. Maybe it got nerfed too hard. Also has surprisingly high DPS which in combination with Shield Restore make it effective against neutrals in the beginning unlike Revelation, Rapture or Halcyon.
Halcyon Carrier - Good ship, useful abilities. Adept Hangar Anima is clearly much weaker than its other abilities. If Telekinetic Push had a short duration it could be used before the masses of strikecraft get in range to fire instead of after.