The PSP, I believe, has four main problems:
#1: Being profitable to Sony.
#2: Battery life when using all of the system features. It's 4-6 hours without the wifi and the speakers in use: sound will likely bring it down an hour or so.
#3: The system doesn't really have a "killer app" that will make people go out and buy the things. GT4 would be a good candidate, but the fact that it is being released alongside (later?) than GT4 for the Ps2, and they are essentially the same game, could prevent it from being THE killer app for the PSP. It could be said that Super Mario 64 DS is already available on the N64, but, after eight years, there is a nostalgia factor that will play into having it, not to mention the appeal of having extras and THE revolutionary first 3D Mario game to play wherever you want. Metal Gear Acid? Close, but no cigar.
#4: The games (who knows about the movies?) cost $50. Can 50 dollar handheld games really appeal to the consumer, even if they are near-Ps2 caliber, especially in the face of $30 games from the competition?
Then again, the thing has these things going for it.
#1: Sony's deep pockets
#2: The sexy design
#3: The power of the machine
#4: Playstation brand recognition?
the DS has these strengths:
#1: New ways to play games.
#2: BC with GBA games.
#3: Nintendo's games, as well as their experience in the handheld market. Mario 64 DS is the killer app for the launch, but if Nintendo wanted to, they could probably shift the focus to Wario Ware Touch as the killer app, or maybe even Feel the Magic from Sega. Mario, Animal Crossing, Pokemon, the Wars series, Fire Emblem, Wario Ware: Nintendo's franchises all are very powerful in driving sales.
#4: A SLIGHTLY better 3rd party lineup than that of the PSP, so far.
#5: System and game prices are cheaper for the consumer than the PSP.
The Cons of the DS:
#1: Not nearly as aesthetically pleasing as the PSP.
#2: Use of the DS' features, such as touch screen and dual screens, may not be that creative in the first year of the system, as developers need time to get used to the new features and to figure out ways to utilize them.
#3: Not as powerful as the PSP.
#4: Despite the marketing, Nintendo still has a kiddie image. Can they shake it off? Does it make a difference in the portable market? We don't know, we can only wait.
Both Sony and Nintendo are giving it their all with the DS and the PSP. Developers are fairly split between the two for the most part. It should be an interesting battle.