They're apples and oranges, really. GTA:VCS is not necessarily "better" (it does have better graphics, though) than Payback, they are different games with different missions, storyline, and gameplay. The PSP isn't "better" than the GP2X, the GP2X isn't "better" than the PSP, they're just different.
The PSP has (somewhat arguably) better hardware all around, and a whole lot more commercial games (as in the kind you buy). The GP2X has a lot of (free and cheap) homebrew games, and on the whole it costs less to have an enjoyable experience with GP2X in my opinion. Both have good emulators (if you're into that sort of thing, it means simulating other game consoles so you can play their games), however in my opinion the GP2X emulators are more polished. As I said, the PSP is more powerful, so if you want to emulate the Playstation you should go with the PSP. The GP2X is not a "plug and play" system. Most software is pretty easy to install (but none of it is idiot proof), for more advanced stuff you have to tinker a bit. Both are good with music and videos.
To put it as simply as I can, if you're interested in wacky user-created games and reliving memories of retrogames, then the GP2X is for you. If you're interested in fancy graphics above all else and 99% idiot proof operation, then by all means go for the PSP. Don't expect either to emulate the DS, PS2, PS3, Xbox, Xbox 360, Saturn, Dreamcast, N64, Gamecube, Wii, Windows, etc, etc, because they can't really.
