I recently bought a DS and have owned a PSP for some time. I dont prefer either per se, but I'll often be in the mood to play one or the other. The quality of games on the DS are more in the spirit of handheld gaming, yet the PSP has a lot of games on offer that rival any console game interms of quality, graphics etc. It all depends on what you want from it, I will say though that the DS has a lot of games which seem easier to play (control wise and in the way they are easy to just pick up and play a few levels) and would probably be better for your kid
