Ima go ahead and mention these 2 monster posts that go rather deep into phase missles and capital ships. It was intresting to reread these 9 months after i wrote them, and I am not sure I still totally agree with myself. (close, though) That said, I think they are important topics for the subject of balance with a good amount of input from others.
That said... in general... and in relative terms... (aka, if you dont want to nerf vas, just slightly buff tec, and buff advent)
Vasari need to be slightly nerfed.
Tec is relativly fine.
Advent need a little help.
Also, in relative terms, capital ships seem a liiitle weak.
carrier caps are a little strong... skirantra is OP.
(for more cap ships, see those above links)
Also, in relative terms...
TEC pacts seem a little strong. (missle pact to a vasari ally is rediculous... change to a damage buff and not a phase missle buff?) May I suggust that supply pacts be a % of current supply, instead of a +800 (so, +40%)
Advent diplo curises and pacts seem a little weak. (have beam pacts affect vas wave weapons?) (culture pacts give... small increase in culture bonus? (antimatter regen, shield mitigation, damage) (or, VERY small +cultue creation on planets (elimating need for broadcast centers if not unde cultural attack... a single enemy broadcast center would EASILLY overpower such an effect.) The curisers are really kinda need some sort of help.
Vas diplo cruisers seem a little strong. (The cruiser gets its most powerfull ability as its first ability... others are kind meh, often not worth reserching.) The pacts are all rather nice. Switching the second an first ability on the research tree seems appropriate.
Most likely far from last thought:
Vas have historicly had a very very stong end game balanced by a weak early game and non-synergizing capital ships.... currently they have both a strong early and end game.. hopefully mostly due to skirantras.