I have both the PSP and a GP2X. I know many people can't afford or simply don't want to buy both. That being said, both systems are nice and have a lot of future potential. However, the difference between the two lies in where their potential will go.
The PSP will, at some point, undoubtebly have sold commercial games made for it. The quality of commercial games on the PSP won't be matched by the GP2X. Likewise, the movie player should remain better than the GP2X (man, is that a nice screen for movies on the PSP) and, of course, the PSP will have internet access which the GP2X (at least in this iteration) won't.
That being said, I see some ultimate limitations to what will be available in the homebrew arena ... particularly if you want to buy new games as they come out and need to update to play them. Sure, homebrew cracks will plod behind, but who wants to wait months (or longer) to play that hot game they REALLY want? And, while the PSP screen is wonderful for movies and the commercial games, it sure has some limitations for emulation quality.
The GP2X will never have the commercial games or the same movie quality as the PSP. But, its potential on the emulation and homebrew front is infinitely better. The system is made for homebrew ... and that is the key feature. I have little doubt that the GP2X will end up being the better machine for this purpose. Not to mention, with continued upgrades, the movie, music and e-book reader (while maybe not top tier) will be pretty good.
If you want to buy a system to utilize ALL of its features (and can only pick one), I think the real question is whether you want better commercial/current games and high quality movies/internet or if you want a top end homebrew and emulation machine (with serviceable movies, e-book, etc). Answer that question and your answer as to what you want to buy is made.
I use my PSP a little more right now. But my GP2X use increases daily as the development advances (and it is advancing rapidly). I can see a lot more of my time going to GP2X for emulation and homebrew purposes as the development matures. I just hope firmware fixes can shore up a lot of the shortcomings that people believe firmware can fix.
I like both. I have both. I guess I am a fanboi of both.