Even though both of these devices are for different types of gaming and can't really be compared, I'll have to choose the PSP. It has better games an graphics! I also like the fact that I can get my music and pictures on it and with the DS I can't really do that.
The PSP has better looking graphics in my opinion, but I like the game series they have on the DS more (such as Pokemon).
Now with both the DS and PSP at the end of their lives, with 3DS already out and Vita coming next month, has anyone's opinion changed? Anyone want to give their final verdicts to this age-old question?
I still think DS had more GOOD games whereas PSP offered what I'd class as the BEST handheld games of this gen. Both had a massive library of bad games too. DS without custom firmware limited itself compared to PSP without custom firmware. Both were a lot better with CFW (I had radio apps, homebrew games, could play my ps1 games on PSP, could play GBA roms on it etc plus cfw supported other video types to mpg4 so I could access more media) So I still don't believe there was a clear winner, PSP has Crisis Core, Monster Hunter, Peace Walker and a few other AAA titles, whereas DS provides a lot of A titles at the expense of few AAA. Both have a place in my heart and on my gaming desk :)
For the most part, the DS won for me. I played it a lot more and brought it everywhere with me and... I own like 3 of them (one shared with my brother, my own Lite, and a DSi because my Lite was overused). I've played my PSP a lot more recently but that's because I've been trying to catch up on the good games I missed--I've played all the amazing titles on DS and there's not much left for me on it now. So while the PSP has gotten a lot more playtime very recently, I think my alliance goes to the DS. Though if I had to pick only one to play ever again, PSP would win because it has Birth by Sleep.