Heh, I just saw something on E3 live 2005 and the Microsoft guy said that the 360 will be compatible, "With our most popular titles".
Speculation is that it will not be completely backwards compatible but that you will be able to run SOME games, like Halo and Halo 2, on the 360 after downloading patches for each game.
A little sneaky how the guy said it WILL be backwards compatible and then attached the little blurb at the end, that not too many people heard cause they were cheering or something.
As for the game gear I don't think it was much competition. People saw the battery comsumption and backed away. The reason I stated the NGP is cause it was caable of backwards AND forwards compatibility (I'm speaking of course of the Neo Geo Pocket and the Neo Geo Pocket Color which both could play ALL Neo Geo Pocket and Color games).