I belive the GBA version (Elite - A New Kind) is the best one. It uses a very similar control scheme to the NES but looks better and plays like the BBC original.
There is also Elite AGB for the GBA. This is an enhanced version of Elite with lots of new ships, weapons, missions, etc and is also very good but is quite hard.
Both of these GBA remakes were done by Quirky.
If you don't want to go down the GBA route then NES is the next best option for a handheld. It is a bit easier than the original Elite and you can pay to dock if you don't have a docking computer. It is difficult to use any of the home computer versions of Elite on the GP2x due to the huge number of keys required to play the game.