"Acronym battle! DS vs PSP!"
linfan691 Q will the ds beat the psp?
It depends, linfan691, on what you're talking about. Like could the DS beat the PSP at arm wrestling? Or chess? This is sort of like wondering if Batman could beat Spider-Man (he totally could too and all of you who argued that he couldn't are wrong--you know what I'm talking about).
But in all seriousness, I'm going to assume you're talking about "winning" control of the handheld market. Well, the DS has quite a lead on the PSP thus far.
According to vgchartz.com, the DS has sold 48.83 million units thus far worldwide. The PSP has sold less than half that at 22.84 million units worldwide.
So in terms of the hard numbers, the DS has the PSP beat. The delta is so large that the PSP probably won't ever catch up to the DS but with the upcoming redesign and the awesome games that are coming out for it, you shouldn't count it out.
In the end, the DS will probably outsell the PSP up to the end of its lifecycle but both handhelds have their strengths and if you can swing it financially, I recommend you pick both up. You'll never be bored on a car ride again.
Hope that helps.