I think it's great that Sins manages to have 3 unique races that are rather well balanced. So far there are things I like about all of them. I don't play MP, just against the AI and I haven't had the game for too long. Still, I tend to cycle through the different races on each playthrough.
With the TEC it's great getting to the point where you can pump out units at a great pace due to a strong economy and fast build times. I find it easiest to put together balanced/coordinated fleets with them. The starbase is extremely useful with its strong trade-port and fast-factory. The cap ships are really hit and miss, with the Mazra and Kol being great, but the others a bit on the 'meh' side. The robotics cruisers are one of my favorite units, except when the hostile fleet has 'em.
I like the Advent because of the cap-ships and the culture war aspect. The cap-ships are a lot of fun to play with because of their coordinated abilities in addition to some decent stand-alone special weapons. The defenses are another favorite aspect as I can set up a planet to fend off most any attack. Even an asteroid can be surrounded by enough hangars/repair bays/beam turrets to withstand late-game pirate attacks with little or no attention. Plus, locking down planets with culture is both an offensive and defensive treat!
I have probably played the Vasari the least, but I do like a good offensive powerhouse! The cap ships are my favorite in the game, easily. While I like the Advent caps for their combo attacks, the Vasari abilities are just useful across the board (for the most part). The phase gates make for some great additional strategy and I like how powerful you can make phase-missile attacks. It might be strange that I find its starbase my least favorite. Yea, it cam move and it's wicked powerful once upgraded, but I don't like in it's role as an offensive weapon.