I personally prefer the ds. Its easy to use and its smaller then the PSP. The DSI doesn't have any slot-1 cards yet and PSPs can be difficult for computer illiterate users.
DS and DSI is the same thing, the adverts with adults amusing themselves by taking dumb pics of themselves and morphing it is just bogus. the DS is better imo, psp has only a few good games and thats if your into shooting games, ill stick to my mouse and keyboard for that. psp is good if you want a internet browser to use away from your pc if you aint got a mini laptop
The Ds with an R4, the emulation programs for psp is really a pain for me and the game files are so big. To be honest, this generation of handheld consoles are terrible in my opinion and not worth the money even with the easy access to games.
PSP over the DS i have both n i only been playing on the PSP not so much the DS its for the PS1 games love the old games