Ok, i have both and throughout the time of owning both consoles i have found the DS to be better in the long run as there has been more games of interest on the DS and better games at that. the DS games seem to be more open where as from what i have found the PSP games tend to be mainly things like sports and racing,in which the majority of people i know are put off by.
Also i believe there is an additional DS cart with a SD slot which can play videos, music, surf net and other stuff.
On a hole, i strongly reccommend the DS, i only seem to use the PSP for internet and monster hunter (most recommended if you do get a PSP)