The relationship of the amount of force on the board to the amount of space on the board is important to the character of the game, the "feel" of the game.
More force makes the game shorter in terms of number of moves per average game, but it also means that you have to think more for each move. (The game is more strategical than tactical.)
All of my old variants, from the 1970s, were designed for postal play, so they had a higher ratio of force to space than you see in FIDE chess.
The amount of force on the board must be measured relative to the strength of the King.
Many of the 3D chess games I've seen have extra space added to the board, but use the normal allotment of pieces, or only a few times the normal amount; I feel there is too much space for the amount of force.
In order for Pawns to feel like Pawns, they need to form an unbroken line at the start of the game; in 3 dimensions, they need to form an unbroken vertical plane.
This is okay, and perhaps a 3x8x8 or a 4x8x8 game would actually be easier to play; but, once again, I have to stress that I'm searching for a 3D Chess, not just a chesslike 3D game.
I am pretty sure that 8x8x8 is the only correct size for 3d Chess.