In my opinion, one isn't really better than the other. It all depends on the situation. The PSP is very impressive, but as most people know, it's very expensive. It's $250 for the system alone.. You can't even do anything with it yet, and you've spent close to $300. If you buy a movie you add another $20 to that, buy a game, add about $35 more. If you want to have a decent amount of MP3's on the system, you'll want at least a 512 memory stick.. so you can add another $80 to that. If you want to transfer said mp3's from your computer to your PSP, you'll need the USB cable, which is another $10. So know you can listen to mp3's watch 1 movie, and play 1 game all for a measley $395. Don't get me wrong, the system is awesome, but my budget isn't. There are tons of other accessories/media that I haven't mentioned that can easily allow you to spend over $1000 for your system.
The DS on the otherhand is much cheaper, it's only $150 for the system, and an additional $20-40 for each game. Most of the games are pretty cool, and feature a lot of interactivity. In my opinion, the DS still isn't nearly as entertaining as the PSP is (Yes, I've played with both). The PSP has better graphics, and more capabilities, but becuase of that, costs much more. Also, if you already have an MP3 player, and a portable DVD player, then the PSP isn't worth the money. At that point it would be better to get a DS, which while cheaper, still has some great games on it, and backwards compatibility with all of the Gameboy games.
There is no right or wrong answer, it all depends on you.