In my opinion the psp is way better than the DS, unless your a big Mario fan. With the PSP you can download music store photos download movies and surf the web. Not just that but you can also watch UMDs on it. And they have not all but pretty much most of the new movies on UMD. The variety of games for PSP appeal more to adults, and the DS is more for kids.
Very bad misconception there ... the DS can do all that also. It's just more homebrew reliant, but Nintendo does have products coming out that fully allow the functionality. I prefer my DS Lite to my old PSP, it's much more portable, better battery life and a load more games out if you remember the whole Advanced library, along with the DS library. The touch screen does add more depth, too.

I got quite a few slow downs on my PSP, and never have had anything like that on my DS.