I have both, but really my PSP could desintigrate into dust and I probably wouldn't notice.
The DS is just better for games, the games are much more original and fun. The PSP is simply trying too hard - LocoRoco was ace, but that's it. GTA on the PSP is hugely impressive and enjoyable. So that's 2, count the other GTA game and you have 3, add in the MXvsATV game and that's 4 - 4 games worth playing on the PSP.
I have no idea how many dozens of great games I've played on the DS. Currently Sega Darts is top of my list, it's just an amazing rendition and very challenging - it looks like it should royally suck, but I don't even like darts much yet I'm addicted. Sim City DS is pretty cool too although you only get to save 1 city at a time.
The best thing about the DS though is it's so versatile - I mean can someone explain to me why they only have 1 analogue on the PSP, and it's on the wrong side! - whereas the DS takes handheld FPS and makes it possible, Metroid on the DS is a testimony to how capable the DS is. BTW, on Metroid you can easily just join a 4 player death match, and before you know it there's Quake3 nostalgia all over the place. Jam Sessions is coming soon too - a guitar simulator that could even be played with a pick, I think that's gonna be huge.
Retro has a nice place on the DS too, DSSpeccy rocks, you get a little keyboard and the games play at full speed, it's well worth getting some old speccy classics on your DS.
I used to give the PSP the benefit of the doubt before buying one - now I see them for the chav accessories they really are
. People seem to rely on that wide screen and the fact it can play MP3's to defend it - well it's by SONY!, and remind us how much it costs for a 1gb card for it. The 1gb SD card I got for the DS cost me £4.
EDIT: Just noticed Lost Magic being mentioned. How mad is that game! - you have to rub sticks with the shoulder buttons and blow on the DS to start a fire, Ray Mears style!. I never got very far, the second one is distracting me, might get that and see if it's any less of a nightmare to survive
.