I would be very surprised if there is an overpowered faction. SoaSE was delayed SIX MONTHS to work on it, since the developers thought that they needed it.
Also, each faction has its own advantage. TEC has economy, Vasari has phase (including phase missiles hehe), and the Advent has culture. if used correctly, culture should make up for the weak T1 and T2 ships and the wait for T3 to make the LRM frigate. The TEC player should invest in trade ports and refineries. If one hasn't unlocked trade ports and refineries by the late game;
a) you deserve to lose
you aren't using the full potential of the TEC, PLAY AS ANOTHER FACTION!
Once you have built a large number of money-earning structures, take a couple random planets and build novaliths. That is the other benefit of the TEC. Seriously. Trade ports, refineries, novalith(s), and you should be fine.
If that doesn't help, play solo against a hard or unfair AI, make a save somewhere in, and experiment.