As a proud owner of a DS Fat, I can say hands down that a DS is the only way to go.

1) Cheaper by a considerable margin
2) Stronger library (consistently better titles out there)
3) Load times are short
4) Nintendo knows the DS is their powerhouse device, and will continue to support it.

I can honestly say I've bought more games for my DS in the two years I've had it than for both the 360 and my PS2. The Phoenix Wright series, Mario Kart, Yoshi's Island DS (excellent platformer by the way), Trauma Center, Meteos, and the list goes on. There's variety with the DS that you really couldn't get anywhere else until the Wii.

The PSP "allows" for some great customizing, but you'll have to put a lot more time (and some money) into it to really get everything you can out of it. The DS, jam a cartridge in and go.

Battery life is a concern too. The DS defeats the PSP pretty handily on that one.