Making me pick one is frankly not fair, but I shall.
Not picking the Halcyon is hard, but I have to say favorite and most useful: Mothership
The Mothership brings THREE great abilities to the table and one so so ability (the lvl 6 ironically)
You undervalue the colonize ability of the mothership if you think it's worthless. The colonize ability on the mothership lowers the cost of planet upgrades by -20%,-40%, and -60% respectively as the ability is leveled up. This is a HUGE stimulus to early game advent economy. Not as much as nicely placed neutral mines but still an incredible bonus to advent.
That ability alone makes this ship the most effective capital. Oh? but that's not all it has.
The ship also has malice. I know malice got nerfed in 1.05, but it's still unbelievably strong. It's a shame this ability is on the mothership, because I never use it. That's because the mothership has one more ability that's even more useful than this one.
Shield regen is an ungodly boost in strength to an Advent fleet. It regenerates shields for EVERYTHING in the fleet, including allied units. It keeps all units alive so much longer. I just love it.
The level 6 is the only ability that leaves you wanting more, but it's actually one of the most powerful in the game, if you every actually have to use it. When you have a match where you actually lose a level 10 cap, you don't have to go back and retrain another. You can just give it the experience from the cap you lost. This is the only race that has such an ability.
All four combined make this the best capital. Period.
I love the Halcyon. Absolutely love it and the aura is so nice, but doesn't compare. Revelation? Amazing ship, and I love its disabling ability, but still doesn't compare, though with provoke hysteria it's a closer battle, mothership's still better though.
