Well, none of them are really tailored to certain needs. Hell, any of the apps for any of the platforms can be cross-compiled or rewritten for any of the other platforms, XGP included.
Well, within the limitations of the hardware in some cases. I really don't think the GBA would be superb at playing movies and Homebrew on the PSP is a pain in the neck apparently. The GP2X isn't a 3D powerhouse, and Nintendo DS' screens are rather strangely proportioned for some titles. Every console has it's shortcomings, even the 2X. The XGP will surely have it's little strengths too, but for everyone who's got what they need or have a particular style of handheld picked out, I'm sure there's already a model out there that does it well or well enough. If I knew nothing about handhelds, I would probably go with the PSP or GBA or NDS, cause they are well established. If I knew a lot about handhelds, I'd be looking right now at what's available for titles, homebrew, ports, etc.... The GP2X is already out and the problems are mostly fixed. The XGP is scheduled for released not anytime soon, and the final release specs aren't full decided if I'm reading right.
GP2X - Joystick is hardly full quality, replacements are being sought.
XGP - Joystick is analog, replacement is being considered. This IS honestly the worst control scheme for most games designed for dpad-style play.
So far, XGP has only seemed to win over those people who COLLECT handhelds or want to code on all possible machines/PSP clones from what I can understand