I just got my PSP, and here's my brief usage description of both consoles.

PSP: Big screen, great video quality, great video streaming, great internet capabilities (browser + internet radio), oh and good gameplay too, thought I don't play that much.

DS: Excellent games library, pickup and play type, stylus control means its accessible to anyone AND it can be used for other applications like the new KORG DS software, language coaching titles, etc. But I love it mostly for Colors! The best homebrew paint program on any portable ever. I use that a lot.