We have one of each. My 9yo daughter has the DS and my 7yo son has the PSP. Now they saved up their own money to buy them so maybe that has something to do with how they take care of them but they are both good for their own reasons.
PSP... has a built in memory slot so you can put demos, music, movies, or anything like that on it. Good graphics, easy to use, good back light for night time.
DS has the 2 screens but no memory slot and the graphics are not as good. With the DS you can get the Games and Music cartridge from Walmart for $20 and then you can put things on the memory card that comes with the cartridge. There are a lot of home brew games plus emulators for other game systems. We have a Pokemon game for the regular game boy that won't fit into the gb slot on the DS so I got a gameboy emulator called lameboy and downloaded the rom for the Pokemon game so that my daughter could play it. Keep in mind that this is only legal because we actully own the game that the rom came from. I would never condone downloading the roms that are out there for every game boy game ever made and putting it on the DS.
So a lot depends on the games you want to play. Both kids the LocoRoco demos for the PSP so that is one of the games my son is getting for Christmas. If you want good quality racing, fighting, or adventure games the PSP is the way to go. If you want things like being able to load the drawing programs to use with the stylis then you want the DS with Games and Music or a similar memory cartridge.
One other thing. The kids love watching movies on the PSP when we are in the car and they are tired of playing games.
One last thing. The new PSP has a TV output jack so you can play the games on the TV when you are at home. At some point my son will probably end up with one of those and I will take his PSP.
