Note: I haven't played through much of the X-COM Files, through I played a nice chunk of FMP. Don't spoil me.
As we know, psi in X-COM ins't perfect. Mainly, it relates to player use - psi is not really very limited by anything, so the player can just scare or mind-control aliens en masse and generally use psi better than the aliens. It doesn't really take many resources and such.
(did they fix the "AI psi focus fire on the psi weakest soldier" AI bug? I know a guy who had a mod which did that for the original game)
Some ideas I had:
1. Line-of-Sight Psi for the player, traditional psi for the aliens: Pretty much what the title says. The aliens have psi for hundreds, thousands, maybe even millions of years. X-COM picked up psi yesterday - it was a know phenomena on Earth, but considered bunk. To the aliens, tho, its estabilished science.
2. Psionics Tech Development: The aliens use psi with cybernetic amps or even no amps, humans have to use the psi amplifiers (mind benders in apoc). Then we pick up the tech and know as good as them? Seems preposterous. Instead, it would make more sense to have two or three levels of psi amp tech.
4. Psi resources. The obvious resource here are bodies of psi-active creatures - Sectoids (especially Leaders and Commanders) and Ethereals.
5. Psi weakens with distance. Of course, alien psi probably should't do that, because screw you player.
6. Psi charge. In Apoc psi spent psi energy, but it expended TOO much energy for not enough return. I think the simpler thing is to just use stamina for psi. Alternatively, use morale like dog does.