If you want to buy a "gaming" (lololololol) PDA that has more shovelware than ds and wii combined, go for the ipod touch. It's portable wifi is nice, but I don't want to surf the next on such a small screen. The app selection may be nice, but as I have mentioned, the ratio of good apps and useless apps are incredible. Oh, and it's music playback is quite nice, though having to use a program to upload songs onto it isn't a thing I enjoy at the very least.
If you want typical Sony bullshit, with terrible media playback, mediocre at best internet browser, and a very few number of good games, go for a psp. After owning it for 4 months, the games it offer are incredibly limited. However, it has some excellent emulators that work quite well. Besides the emulators and those few good games, I'm not terribly happy with my purchase.
Depends on what you want. If you want a proper mp3 player with a few decent time killers, go for an ipod touch.
If you missed out on years and years of gaming, but don't need an mp3 player, go for a psp. Oh, and psp has games too.