Drinky got yer reasons down nicely.
Anyway as a proud owner of both handhelds I must say the PSP is much better in terms of multimedia, music, movies, etc.
It's easy as fuck to pirate psp games btw. If you aren't going to downgrade your firmware/ use a custom firmware you might as well not buy one. PSP has a sexy screen, and the D-PAD is FINE. Plus you can get a nub attachment for like 2$ off ebay if you are some sort of nfag whiner.
Edit: Also its an emulation MONSTER. Near perfect PSX emu, SNES, perfect NES, GBA, Sega Master System, THE LIST GOES ON... but nintendo fans are used to paying for roms anyway so you may not like it.