The big problem with the PSP is that 1) Western gamers don't want to play home console games on a handheld. Western gamers want to play different games on handhelds and Nintendo gets it. That's why the DS has it's own identity and offers a different experience. The PSP is like a "me too" system, trying to compete with home consoles but it can't. The DS is more of a complimentary thing. It doesn't compete with home consoles, it offers a different experience. If I wanted to play GTA, Ratchet & Clank, God of War, etc. I'd dig out the old PS2 or buy a PS3. The DS takes advantage of the stylus/touch screen and also goes for that retro/vintage edge.
And 2) the PSP's biggest advantage (great old-school jrpg/srpgs) is negated by the sheer size of the DS' jrpg/srpg library.