I like the Advent the most because, well, they are the most aesthetically pleasing. At least that's why I started playing them initially, and since I learned the game playing as Advent, I have by far more experience playing with them.
The TEC is also fun, especially on smaller maps, but my general RTS playing style favors a realitively small but powerful tech heavy or hard hitting force.
I thought I would like the Vasari, but to be honest I never have much fun playing them, probably because I absolutely hate their game music. I've been meaning to try to swap their music with some "battle mixes" I made to see if I enjoy playing as them witjhout that limitation.