PSP wins my vote by a large margin!
PSP by far.... I own both a PSP using firmware 2.0 and the genius EBOOT Loader, as well as a DS. I don't own a GP2X so I admit I will be somewhat biased towards the PSP. Although I've read a lot about the GP2X and especially comments from owners of the GP2X.
Its my opinion that the DS is not even in the same league. It is great and intuitive in its own way but it does not get used nearly as much.
Thanks to some very smart and dedicated people I stare in wonder and amazement which is renewed almost daily due to the PSP's design, versatility, and very talented homebrew developers. I can watch great quality AVC video content, play some good UMD games such as GTA, Tokobot, Legend of Heroes, Popolocrois, etc. or indulge in nostalgia and relive a big part of my childhood thanks to many quality emus. To play such classics as Zelda, Chrono Trigger, and Final Fantasy etc. on the PSP is a highly rewarding experience.
Its not just about what games can be played or what emus are available. Its the look, feel, and great design of the PSP that enhance the experience beyond what any other handheld device can. The ergonomics, the screen, the button layout compliment the high quality of the emus. With full screen support, good sound, and pixel smoothing abilities, a lot of games look and perform better on the PSP than they did on their originally designed ancestors to the PSP.
Basically to have hundreds or even thousands of games on a duo card about the size of a postage stamp gives us freedom to relive just about every era of gaming history in an elegant portable way.
Sorry this post is so long, I just can't say enough good about the PSP. There are unfortunately a couple bad things I need to gripe about:
1.) The LCD ghosting drives me nuts --> Not so much with homebrew but with UMD games and videos. Also many left with dead pixels. Very disconcerning.
2.) Ridiculously small amount of storage space --> More insulting is that the PSP is a multimedia device which can play music and videos right out of the box. The 32MB duo stick was a joke and a slap in the face. With 1GB being the largest readily available memory stick and 2GB being crazy expensive and hard to come by, I am increasingly aggravated that such a multimedia capable device has such limited storage solutions. I could live with an affordable 4GB memory stick pro duo but that might be wishful thinking.