[douglas]

This is all going on memory, but I'm pretty sure it's accurate and complete.

Psychic races get:
System training facilities; their maximum training levels are no greater than those of the sector training facilities available to everyone. Yes, they do allow for slightly faster training (one of them will stack with any normal training facilities for 3% more training per turn) and greater flexibility in where you keep your ships while still at least training them slowly, but normal races can still match the final training levels with only a minor delay and less flexibility while training.
Psychic sensors; who cares? Hyper optics are so cheap to research anyway, and available to everyone.
Normal damage psychic weapons; no big deal, they're not exceptionally good.
Allegiance Converters; very powerful, but there is a perfect counter that every half-decent player should know about and have available before long, even without the threat of a psychic race present. Master computers render this special weapon completely powerless, and are a side benefit of getting robotoids and computer complexes, which are essential economic techs.

To sum up, psychic races do get some decently good stuff, but none of it is both ridiculously powerful and non-counterable. In fact, I personally would not take the psychic race trait in a competitive game because I don't think it's the best option for the 1500 points it costs, even in a 5000 point game.