The PSP, IMO, has huge potential via USB sticks. But, AFAIK, nobody has broken the PSP's encryption. The possibility of having multiple USB sticks holding various emulators and games, is just mind blowing.
It's a powerful little machine, much more so than the DS, and has a far superior screen thats just begging for emulation.
On the other hand, it looks as if coders are getting to grips with the DS, and the encryption isn't far off being totally cracked. Wi-Fi, holds a lot of potential for emulators, especially multiplayer emulation. I'm not sure about dual-screen being anything useful in regards to emulation, but could be for homebrew games.
You also have the ever maturing GP32, which has a major head start to both the others.
It has a nice screen, if you opt for the back-lit version, and a fairly good battery life.
Tapwave's Zodiac, looks powerful and full of potential. But way too expensive for a handheld, and probably will end up going the way of the N-Gage.
My money is on PSP. It's got Sony behind it, a fairly nice price point that will drop in later months. It's very powerful, and the screen is just gorgeous. The battery life is no deal whatsoever, and mine will easily give me 6 hours of ridge racer. The analog control stick works a treat, and neither it or any of the buttons, get in the way of the screen. Most of which are blown way out of proportion from Anti Sony, Pro Nintendo fanboys.