The Tec have good armor but weak shields. Their strength lies in their economy which can really help mid game. I like the TEC for their long range combat abilities (especially the novalith) but their culture spreads slowly which can hurt your economy.
I like the vasaries armor and raw firepower they can bring to bare on an enemy. The phase gates allow for great manuverability and hit an run attacks. The main disadvantage is a weak culture and mediocre economy.
The advent have some great abilities (clensing brilliance, malace, etc.) their culture spreads faster than the other factions which can be useful and they have good firepower after its upgraded. Some of their ships can really make any fleet pack a powerful punch (illuminators) The disadvantage is that the advents economy sucks and you need to almost constantly research upgrades in order to survive.