The main thing to remember here is Nintendo is known for it's handhelds. Hands down, they've shut out all others that try to compete. However, with the onset of these "nexgen" handhelds we have a problem.
The game companies are now getting handheld into the realm of 32bit. That's pretty spectacular. That in mind, Sony has had the console market cornered for years and has only recently, with the introduction of the XBox, lost some footing.
In short, you're looking at two top-notch companies with solid backgrounds and plenty of cash. The only way to find out which is better, DS or PSP, is to go and try them out for yourself. Either one is a good choice.