if you want RPGS + PUzzles go with the NDS
if you want Action/FPS/adventure go with PSP
although that isnt to say the NDS hasnt had some good games because these are some of the good ones:
Final Fantasy games
Metriod Prime: Hunters
Mario 64 DS
Mario Kart
Brain Training-type games
Zelda
GTA: Chinatown Wars (to be released soon)
Worms Open Warfare 2
Sim City DS (basically Sim City 2000 converted)
oh! and Resident Evil Deadly Silence (which is a complet remake of the original game with a new game mode where its all changed)
plus...there is a special card you can get for it which allows you to....you know....*cough*download games*cough*
did you know it is shockingly small how big (size wise) the games on the NDS are :O Final Fantasy IV for the NDS is only 100mb
cant say much about the PSP as i didnt have it for long and it was awhile ago