I have both a PSP slim and a DS. Thing is, the PSP is much more powerful than a DS but the games for the DS are more cooler and more fun. I think I just prefer one or the other sometimes.
It really depends.
Its when really good gams come out for PSP or DS that I begin to prefer one of them. Like when Socom 1 or 2 came out, I
loved the PSP. And when Metroid Prime Hunters came out, I loved the DS.
Some pros about PSP that I really care about:
1. Built-in browser: Not one of the best ones out there but its still there. You gotta pay for the DS.
2. Games look awesome-er in the PSP compared to the DS.
3. Can play music/movies right out of the box without hacking anything.
Cons of the PSP
1. Not enough games
2. Terrible speed of the browser+loading times of games.
Pros of the DS that I really care about:
1. Has much more fun games, I think. Mario Kart DS and Metroid were kick ass during their times and Wifi was really fun...ah, the good ol days.

2. Touch screen.
3. More variety in games
The only cones are that games dont look as good as the PSP but oh well. They are still better compared to most games for the PSP.
By the way, anyone know of any other good games for the PSP? I like online games, shooters, action and adventures. Not really a sports kind of guy. I played Socom 1+2, Battlefront II and Renegade Squadron, Wipeout, Bounty Hounds and Kingdom of Paradise. Yeah. That's basically it. I've never found a really good games and right now, my favorites are just socom and wipeout.