Here's my two cents and a whole lotta rambling on the upcoming battle:
The handheld market has been controlled by Nintendo ever since its inception. Nintendo has had a hold on that market longer than any other company has dominated the console market. People think Game Boy when they think of handhelds.
The handheld market has turned into the most casual market out there. People buy the system 'cause it's a lot cheaper than the others (and so are the games usually), and only a couple games because they know they won't be playing the system a whole lot.
As far as the DS goes, if Nintendo can make someone make it go online, and advertise the hell out of Pictochat, the system will be a huge hit with the casual gaming market- and others who usually don't use video game systems (like say a parent might not want to get their kid the DS, but it has "AIM" [Pictochat] on it [or so the store employee describes
]- this would likely push towards a purchase). The system is not going to go over like the GBA SP and GBA did at $150, but it should sell pretty well. Nintendo games being $30 will be a potential plus.
With the PSP, I'm not sure what Sony's up to, but I think it's possible they're building drama and anticipation for the final details of the system. Build the thoughts in people's minds that the system's battery life will be short and the price will be near $300, and then reveal a $200 pricetag (the PSTwo helps me believe this is possible if Sony's willing to lose money), and a decent battery life. It would blow everyone away, haters damned, Sony is awesome, awesome is Sony, etc.
The only thing I wonder about Sony is if they know what they're doing in the handheld market. It's possible that they might come in, kick ass, and change everything around. If they go in treating it like the console market, they may be in for a rude awakening.
And my question for Nintendo is if they have a good backup plan. If the DS fails and the PSP comes out swinging, Nintendo will need to get something out real fast.