PSP from a technical standpoint is better, also really good that you can play nearly all the PSX games on it.
But I like my DS A LOT better, just because I found there weren't a lot of games for the PSP and you needed to do a lot of back-end work to get most downloaded games to play and by the time you had them working you were sick of them, and if you want to do homebrew you have to constantly keep up with the scene.
DS, I find has a lot better original games for and homebrow 9 times out of ten is just download, drag n drop, and play.