My first fleet were The Ancients ('cause it got me a whole fleet cheap & I was broke at the time), so please bear with me as I sound off. I've only had a few games with them, but I & those I play have already noticed a distinct trend.
Crits are a pain, yes, but the auto-repair feature and utter lack of crew are painfully effective at mitigating that. Between them, those two features mean your opponant has to keep rolling the same crit every round, and that an entire crit chart is essentially meaningless (#5 - crew crits).
It's been my experience that the scale of the game determines how well Ancients do. A one-Ancient game is the elder race's to loose. A three-Ancient game, in contrast, will result in a victory for the Younger Races (YR, including Vorlons/Shadows for purposes of this post). It mostly seems to be a matter of number of guns and number of hulls. Sure, the Ancients can soak up the fire from any one or two ships and annihilate whatever they hit, but as the number of Younger Races' ships climbs, there are too many dice being rolled, which vastly increases the chances of a no-speed or no-weapons crit.
The best balance seems to be a Two-Ancient battle. You'll probably loose one Ancient, but the two combined will be able to throw enough hurt onto enough hulls to keep it interesting.
The Lordship (whichever figure you use) has performed the best for me, mostly 'cause of the Hull 6 & Adaptive Armor. The fact that it's got four full weapon arcs helps as well. The Dark Knife is the second best, mostly for the same reasons pre-Armageddon Shadows were - SM & a 30" TD beam. The Traveller's all right, with ridiculous numbers of attack dice, but watch out for it's special ability - if someone gets within 10" they can start trying to ram you even if you've never shot at them (EA tried this w/ a Warlock... thank Heaven for CQ 7). The Thoughforce is... eh. All the attack dice are nice, but it's too slow and the shield isn't as effective as Interceptors or a Gravitic Energy Grid would've been. As for the Triumviron... I'll never use one again unless I'm playing a specific scenario or it's 4-5 Ancient. The uber-cannon's nice, but the ship's even more vulnerable to weapon crits than the rest, as it only has one firing arc.
Bottom line: they're fun, they're scary, they're not at all as powerful as the whiners I play with were making them out to be

. Stick to just one or two and you'll have a good game.