I own a PSP so I can help here. They do have very good graphics for a hand held system BUT with its little size comes a few setbacks. 1) you only have one analog stick. 2) you only have L1 and R1. With out another analog and L2 and R2 game controls can sometimes be very difficult.
I dont like it cuz its games suck. I like DS's games better. Although PSP has better graphics (I AM A SONY FAN) but DS has better games. And i couldnt afford it lol.
PsP does rock Ds games are very cartoony so it depends on what kind of game you like but you can also watch movies on the psp and go on the internet oh and music