It depends on what sort of games you like to play. If you are s big fan of the PS1 then the PSP is your man as it plays "proper" games and has fantastic graphics, in hand-held terms. It can be used as an MP3 player and a video player, so does lots of extra things and has a nice interface.
However, I much prefer the DS as it has cutesy games that you don't have to play for hours at a time to get somewhere. Its perfect for taking to work and playing at lunchtime. If you are a fan of Popcap or Minigames then the DS is your man. I have always been a big fan of Nintendo so this is my handheld of choice - where else can you play Zelda or Mario?? Plus, I love the stylus and microphone controls - brilliant concept; makes playing games all the more interesting as you actually have to do some of the things required to progress in the games. Its almost a Wii in a bag sized case :-)
Supplement from 04/04/2007 09:02am:
"bag-sized" actually makes the unit sound huge lol - what I meant was "small enough to fit in my handbag".
If you get the Lite you also have the added benefit of a "lid" that means you don't really have to buy a protective case for it (although I have an outer that I use so that the case doesn't get scratched). It also goes into sleep mode when you close the lid.
Oh yes, and you can play GBA games on the DS Lite and connect to the Internet if you buy the Web Browser (Opera)