PSP is better for older kids, more PS2 style games. The Nintendo DS is better for younger kids and girls.
Depends on what you want to do with it. If you want to play games, listen to music and watch movies then the PSP is the way to go. I have one and I am 36. I use it for the plane and on trips but you can crack DVDs and put them on the PSP instead of buying them. Also has WiFi capability.
Nintendo DS has a bunch of games for younger kids but is still good for all ages. You can't beat mario Bros. It also has WiFi capability and networking if your buddy has a DS next to you within 100 feet.
How old is your kid/s? Boys or girls.
i don't think you can go wrong with either. Both hi-quality systems.