Im rather suprised that PSP has only one vote so far...
anyways, I voted DS, and here's why:
I own both these systems. I, to this day, think it's unfair to both parties to compare one to the other. A Nintendo DS is in no way anywhere near the same thing as a PSP. A PSP is a portable PLaystation two. Every so often you get some amazing games which arent on the PS2 but GENERALLY, a hell of a lot of PSP games are ports, or are released for all the major systems.
PSP is a good system. THe screen is amazing, sound, amazing. It's cool that you can go online and memory uprading is handy too. However, I bought the PSP and only have purchased two games for it: Me and My Katamari and Valkyrie Profile. Valkyrie Profile is a port from the PS1 game, and Me and My Katamari is virtually identical to the other two Katamari Damacy games. While I claim those both to be amazing games, they're not new and amazing.
And honestly, I NEVER watch movies on my PSP. It's annoying. I get tired of holding it after an hour and a half.
But it IS a good system if that's what you want: a portable PS2 with nothing really new or special (save Loco Roco and Lumines, the latter being released on PS2 anyways...)
Now, DS:
I have not touched my Gamecube, PS2, Xbox, PSP, nothing for months. Why? DS CONTINUOUSLY releases amazing, new, and innovative games. And they are all games from so many different genres, and because of the dual screen, they are games which have not been duplicated or released for all the systems.
Every month SOMETHING comes out. With the DS Nintendo has been really holding strong to it's first party characters: We have MANY Mario themed games, Pokemon games, Star Fox now. IT's also welcomed many other new charcters to its team, like my beloved Phoenix Wright (Which I know isnt new in Japan and is a GBA port but damnit, it's new here) and games like Trauma Centre.
Innovative and new. Cooking Mama. Trauma Centre. Electroplankton.
And taking the old and making it new. Animal Crossing. Star Fox. Super Mario Brothers.
The DS is simply a steller system. I have, because of this system alone, become a huge hand held gamer. Sure, almost strickly for DS, but I was NEVER a hand held gamer before. Now, my other systems collect dust (except for when my Mom plays games)
Theres so much I can say. Both systems are good in their own ways, but for fun factor, I will ALWAYS go with the DS>