I had a PSP for a short while and spent most of the time messing around in homebrew apps. The one redeeming quality I saw over the DS (which I also mostly used for homebrew) was the ability to emulate MAME (namely, marvel vs capcom at full speed). I contemplated pirating a game or two to see if getting a PSP was worth it, but upon searching, I realized there were like, 3 games which I considered worth playing, so I just gave it back.

DS lite + flashcart is the way to go imo. All of your basic emulator bases are covered(short of GBA), you can fit all of your games on one microSD card (as opposed to two or three large games per PSP memory stick), and I've always personally found the DS lite d-pad and buttons much more comfortable than a PSP.

DISCLAIMER: I don't pirate (rather, I do not outright steal games), pirating is bad. If a developer spends the time and resources to produce a game, you should rightfully do your part towards compensating them. This is not a topic for discussing piracy and I would rather not go through the effort of internet-arguing with someone about morals.