Well.....
This is coming from my Beta experience and the current manual and about 5 hours of playing the final release. I'm sure I'll be quickly smacked down if I'm off.
TEC: start out with weaker ships and higher productivity. Since T stands for Trade you'll probably find they have an economy advantage. This is the most straightforward race to play.
Advent: think wizards. They have all the magic stuff, er psionic powers or whatever. I can't say much more than that. There were no Advent in Beta and none of my games have featured them so far.
Vasari: strong ships, lower productivity. The manual would seem to lead us to believe their heavy-handedness and alien pathology gives them influence (fear and subjugation) as well as limits their vulnerability to the TEC's broadcasts of how screwed up Brittney's life is this week.