There are elements of interest found in higher-dimensional chess that are not found in 2D variants. But many think the 2D surface is the best to play upon. Even if the game is 3 or 4 dimensions, playing on a 2D surface is generally easier. For an interesting take on this topic, let me recommend Mapped Chess, by S. Burkhart, found here:
http://www.chessvariants.org/index/msdisplay.php?itemid=MSmappedchess