I'd like to add to this thread beacuase I own both the GP2X and the PSP v2.6
I can clearly tell you if you want to play snes and nes GO WITH THE PSP. The Gp2x does have a full speed NES but the SNES is for lack of a better word "lacking" (it doesn't have full speed nor transperencies) The PSP snes isn't full speed as well but where the GP2X gets ~30 fps without sound in Chrono trigger the PSP gets ~60 fps with sound at 44kbs.
Like other ppl have said the PSP is more expensive but if money is of no concern get the PSP.
Also so this is clear. PSP's have been hacked all the way to v2.71 to be able to play homebrew!!!! this with limited kernel mode (google of you care) Basically if you buy a PSP now you can play homebrew on it.
As for my GP2x I love using it for my Geness+ games as well as my PC ports. But other than that I use the PSP for my Snes games...the emu is incredible.
Hope that helped, if i missed something just ask. I own The DS, PSP, and GP2X. All homebrew capable