I'm a ex PSP owner & current iPhone owner.
I would go for iPhone for some personal reason:
- PSP is demm heavy, my hand get tired if I have to carry it 2hr in a bus/train while watching it.
- PSP doesn't feel nice to hold on my hand.
- To sync the video into PSP is troublesome (during my time), have to install this and that, convert this and that, take out the memory card and put it back. Then I have to remember which movie I watched, watch until where.
With iPhone I just use iTunes. And iTunes manage what I want, clean. iPhone remember where I last stop the movie (very important).
- Quality wise I can comment much, as this solely depends how you do video conversion. And the UMD is ofcourse good. But I don't use magnifying glass to watch a 3.5" video.

What I like for PSP is the animated clip you get when you're picking the video.
If you don't remember what's the title, at lease you can have a preview of what is it.