I have to say DS.
I've played with both of them and I know a decent amount of stuff about both of them, too. For me, the only choice is DS for several reasons:
1. When I look at the PSP game shelf in a game store, it has two or three games I'd like to buy. When I look at the DS game shelf, it has ten or more games I'd like to buy. I'm just generally more in the focus group of DS than PSP.
2. Sure, PSP has an awesome, large screen and you can watch movies with it. However, when you play with it, the big screen is practically the only merit it has. The touch screen on DS is innovative and it's fun to play games with it. PSP only has a directional pad and an analog stick in a place that makes your thumb sore if you use it (that's the same with the controllers of PS2 and PS3. What's with that?). It's just not as much fun to play with directional pad than it is to poke at the touch screen with a stick :laugh:
3. Okay, you can listen to music and watch movies on PSP. For some people, that's a great feature. You know, a portable movie-watching macine for a long bus trip or something is simply an awesome idea. However, when I buy a handheld game console, I want to play games with it. All other features are useless for me. Why should I pay extra for a feature I won't be using? Thus, DS. Of course, this is a fairly stupid point in general, but an important thing for me. That's the same reason I don't want a cell phone that has a MP3-player in it.
I generally like Nintendo's consoles more, because they do the thing I bought them for. They're gaming machines. I don't want to pay extra for a blue-ray player or DVD player or whatnot. I want to play games. I guess it's kind of stupid, but...
From these two, DS is definietly my choice. PSP has some good games and some awsome features, but DS just wins in my case.
Besides, isn't it a bit unfair to ask a question like this on a Pokémon forum? :laugh: Although I bought Pokémon Diamond because it was on DS, not vice versa.