I think now that the prices are nearly even it's going to come down to the games. Who has that amazing killer app that sells systems? Right now looking at the launch lineups neither has it but at some point some game is going to break out. And it won't be a popular sequel either. Killer apps are usually something that comes right out of left field.
As for the other features well both have unique pros and cons that I think balance out enough that they won't be that big of a deal to the mainstream anyway.
DS:
Pros: First party Nintendo titles, better battery life, touch screen can result in games the PSP can never duplicate, no memory cards needed, Nintendo has tons of experience in the handheld market.
Cons: Lacks the PSP's "cool factor", lacks movie and music features for not much less money, weaker graphics, touch screen may not matter to mainstream and needs a killer app to sell the concept, game cards hold less than UMDs.
PSP:
Pros: Very strong Playstation name, superior graphics, analog stick thingy that the DS doesn't have, music and movie playback which although not perfect are still a feature the DS doesn't have, obvious edge in marketing, very traditional design which is more inviting to mainstream types who just want to play Madden on the go, Sony is traditionally better at third party relations.
Cons: Lacks a quality first party lineup on par with Nintendo, doesn't have same third party advantage that PS2 has with the console market, lack of dual touch screen stuff means that a creative DS game cannot be ported accurately to the PSP, rumoured low battery life, requires memory cards, potential skipping issues with optical medium, usual "Sony factor" regarding product reliability.
So both have a fair share of issues though realistically I don't think any are make or break. It's about who gets that must own game out first.