DS wins this for me, I'm a huge, huge,huge nintendo fan boy, i grew up on them, so i have to back them everytime on principal.
On a none biased view, the only thing i like about the PSP is that you can play PES, but its not even online so i'd get bored of it quickly.
As for the DS i love you, I only have four games, but i have hardly stopped playing them since i bought them, games are:
Super Mario 64 DS (a classic and playable over and over again)
Mario Kart DS (Superb, all the fun of Snes and 64 versions but you can anyone in the world)
Kirby's Canvas Curse (what the touch screen was made for, a game entirely based on using the stylus, neat control and special moves plus tons of side games and levels to battle through)
Animal Crossing, Wild World (Similar to the sims only better, Imagine sims but with Animals, create ur own town and house, design ur own clothes, decorate your house, work in a shop, tons and tons of things to do. and now you can join someone across the world to get more tasks to do)
There's no arguement for me, the four games i've listed kill whatever the PSP can do, least forgetting WarioWare Touched, Metroid, Monkey Ball, Nintendogs and new zelda in the works and new Super Mario Bros game due to be released later this year.
Nintendo have also developed a web brower to be work as a cart, simply place the cart in the normal game slot, get a wifi connection and you use the internet via an Opera App.
As for people who wish to get video/images/music may i suggest this: Advance Media Player. This is a device that you slot into the GBA hole in a ds, aslong as you have mediacard you can upload movies/mp3s and images to be played through your ds via this cart. Have alook on ebay as they go quite cheap.