The DS by far. Its library is much stronger than the PSP, and considering the PSP library is quite good, that's saying a lot. The 7th gen was the peak of the dedicated handheld market.

DS. Just so many great games. The PSP is the best non Nintendo handheld ever though imo.

Never owned or played much PSP but the systems design is just so sexy. Probably my favorite design of any handheld console. The DS had more of the games I like to play however as well as playing my backlog of GBA-games.
Skipped voting this time. I respect the PSP to much to vote against it.

I remember fondly how the Psp was ridiculed at the time. Of course the DS obliterated it in sales to much joy for the Nintendo fanboys.
Personally I bought one for Crisis Core and ended up playing loads of Jrpg's on the Psp.
The better one?
No way of determining that.
I'd say we all came out on top with two awesome systems.

Aside from battery life and discs made of egg shells, I don't recall the PSP being ridiculed. What could anyone say about it?

I mean, the NDS has games I would put on my list of best games of all time. PSP has many great games, but absolutely none comes close to that level of quality. Besides, I think NDS has more good games in general than PSP.

So to me is not even close. NDS all the way...

Nintendo DS, of course

PS Vita better than PSP

PSP
Crisis Core, Dissidia, Persona 3 Portable, Tekken Dark Ressurection, Peace Walker - I put so much time in these.

When looking at the actual libraries, niether was a bad option. DS was just, by far, the better option.

DS. You don’t mess with Nintendo in the handheld space. Too many time tested IPs. Pokémon, Metroid Hunters, Advance Wars DS, Golden Sun to name a few.

Sure PSP has some late life sales improvements over DS, but by then it was too little too late