The DS and PSP aren't even comparable. The PSP is a piece of shit until you put CFW in it. It turns awesome when you realize that there are a shitload of emulators for it and that you can now play a crapload of PS1 games. If you use h264, video quality on the PSP is a lot better than you'd expect, so that makes it a decent portable video system.
There are also a couple of decent games for the PSP, most of them being remakes.
The DS, on the other hand, has tons of LOL POINTLESS PUZZLE GAEM crap. Homebrew doesn't come even close, but the fact that you can fit lots of games into a 1 GB cart makes it awesome for sporadic gaming. Then you have the masterpieces like the Phoenix Wright series, Zelda, Mario Kart, etc. If you can be bothered to wade through all the crap that comes out for the DS, you often find interesting games that aren't really worth a mention but are still fun as a passtime.
They're completely different systems, just get both and pirate all the games, you faggots.