Can only comment on Advent:
RadianceQuite ok overall, but in the end it is a "simple" ship. It can kill enemies, and more importantly it tanks out the damage of the enemies.
Be careful of anything disabling/ignoring shields though, for a Battleship the Radiance is extremely fragile.
Animosity + Energy Absorptive Armor for the win however, and then dump the gains into more Detonate Antimatter.
Despite being the main fighting ship, I use the Radiance as support, keeping the fire off my main force, and casting Vengeance on it before taunting. (then the enemy gets a lot of damage back - now put Malice onto the enemies and you see an entire enemy armor slaughter itself in seconds, it has a certain... Imperatorial feel to it

)
RevelationMeh.
That's the Revelation in one word. Meh. Yes, it has great powers, it's Clairvoyance is a lot more useful than what it appears to be, allowing you to use your forces and your Deliverance Engines with pinpoint accuracy, however the enemy can see what you're tracking so be careul.
Reverie is interesting as is Guidance, but both pale besides the supportive powers of the Progenitor or the Rapture.
Lastly Provoke Hysteria is great, but by the time you can get that you are normally well-stocked for planet attacks.
All around still a good ship, but just can't keep up with the other 4. I usually build one midgame for Clairvoyance scouting, and that's pretty much it.
HalcyonCome to papa!
This is
the punch in my armies. Maxxed-bomber Halcyons with their Aura on the supportive ships and firing Anima Tempest skills right after I took out the flak vessels are just evil.
More of the same, the Halcyon may be very passive in nature (with 2 passive abilities), but it's support aura is insanely powerful and it is just purely dangerous. It might not be the Vasari's high-power strikecrafts but the raw mass of what you're sending against the enemy (with Anima Tempest) is scary.
And Push can be very useful. Used manually at the correct moment it can completely block the Vasari's superior strikecraft (people rate it low because they only got 1 Halcyon - get multiple and it's insane!), and by the time they recover a full-Fighter Halcyon completely cleared the skies.
ProgenitorNormally my first ship, it's abilities are well above the others, at least at the start.
Frankly, the Progenitor should be your
first or
second capship. Malice is godlike. It's colonization is the difference between fast expansion and Game Over. And Resurrection is quite nice overall, later on.
Plus it has good direct power and Shield Recharge is (no joke) AE Invulnerability.
RaptureThe primary supporter of the Advent, it has great supportive powers but can do little without an army around it.
Overall this should be #3 or so, it's good once you get your army going.
Progenitor -> Halcyon -> Rapture -> more Halcyons -> Radiance -> Revelation -> more mixed.