I think Nintendo will keep control of the handheld market for now. The hype of the 3DS is seemingly far greater and it's definitely not all about power as we found with the DS vs PSP sales. The fact is, as I'm sure I read WeasteDevil say somewhere in this thread, it's about software. Nintendo's handheld titles are usually a lot more worth it to most people, as they weren't just seemingly scaled down versions of the home console games (although the PSP2 could potentially change this). While the likes of Zelda, Mario, and Metroid evolved into 3D games on the home consoles and have been massively successful, the more 2D versions that stayed on the handhelds sold just as well, if not better. There's also Pokémon, which despite being yonks old, almost always becomes the top selling handheld Nintendo game, or at least very close to it.
However, although I touched upon the PSP2 having the potential to produce similar level graphics and probably gameplay, it's still unlikely to appeal to a lot of people. If you have a PS3, why buy a PSP2 to have what will now be basically the same game, rather than a different one but not as good? I don't think the games on the PSP, that were only for the PSP, really matched up enough. Other than Monster Hunter, I've found it difficult to get into games on the PSP - but even then, as soon as Monster Hunter came back to a home console (Wii) it was vastly improved IMO (though mainly due to the fact the game needed two control sticks badly).
We'll see if some better games make it onto Sony's handheld console this time, but if I'm honest I've seen less and less appeal in getting a Sony console at all for a while now.