I think if Sony really hypes the multimedia aspects of the PSP, it could do well. As is, I suspect alot of consumers are looking at the system and going "eh, it's just a portable PS2". Which while quite the technical feat in and of itself, the average PS2 owner is likely content playing his games at home. I know Sony has stated that the system won't be just a port-over machine, but unless those making the games are willing to dump alot of development cost into the once low-cost handheld market, they're probably going to lean towards converting games, at least initially. What really sales the GBA for me, is that I simply can't play the types of games it offers on consoles. While the three main contenders at home place alot of emphasis on graphical quality, most GBA titles place the emphasis on straight-up gameplay with graphics from a SNES era most of us look upon fondly. Don't get me wrong, there's ALOT of terrible GBA games out there, but there's also been some amazing ones.
Frankly, I think Sony would have been better off marketing the PSP as more of a nextgen Walkman that happens to have great gaming capability. But the closed nature of UMD, ATRAC-only audio support, lack of a digitizer, and alot of other factors prevent the system from really being a MP3 player/PDA replacement. If they really wanted to give Nintendo a run for its money, they should've gone all out and made it a multimedia powerhouse.
As for the DS, I'm tempted to say it's too soon for Nintendo to be releasing another handheld system and that alot of the motivation behind it was Nintendo's fear of the upcoming PSP and an uncertainty that the GBA would be able to compete. Personally, I feel such doubt is unfounded, and foresee the GBA remaining the top-selling system for awhile to come, but what the hell do I know...