PSP will support PS2 graphics...but the games ACTUALLY designed are usually dumbed down. I read an article by EGM Magazine where they comared the systems and showed actual graphics for both...some of the PSP games were beautiful, others looked worse than the DS.
Only beef i have with DS is it is still marketed towards younger gamers with games like Mario (seems kinda kidish)
They still use cartridges so graphics aren't impressive (although much better than previous gameboy graphics)
using cartridges also limits the sound quality of the games...don't expect a symphony. it shouldagain be better than GBA sound though.
PSP beefs i have are as follows:
VERY short battery life, you couldn't even finish a LOTR movie on it b4 it died on you
Price tag is ridiculous, even for the features it has i could get a PDA that lasts longer and can do more (besides gaming aspect)
the controls on it are limited and laggy on most games reviewed by EGM magazine...they said it was ok on some games...but most were unresponsive and clunky.
overall i would get the DS if i HAD to choose one, but i am not getting either of them. Just as i do not wish to get a console like the XBOX or PS2, i don't wish to get a new handheld. My N64, GBA SP, and computers will stay with me forever