I have had extensive time with both and though I feel they both have their strengths, I prefer the DS which is why I actually own one. I feel it has the stronger library overall. PSP needs Homebrew to even be a contender.

Granted the DS isn't perfect and it gets a quite a few games that shoe horn in the systems features (FFIII anyone?) but the PSP has many extra's I don't give a damn about... movies on the go? I don't watch films anymore. Music? I have an ipod for that...

The DS is gimmicky at its worst, the PSP is a schizophrenic piece of hardware that doesn't know what it wants to be at its worst. Yet both have their moments of pure excellence.