Tri-dimensional board games: How does the additional dimension extend possible player requirements & game structure?
While I've not seen serious work on it... I have played trek-style 3d chess

Take the pawn. In 2d, it has one move option. in 3d, given the start locations, it has 2, sometime 3, options Twice that many "covered" squares it can attack to.

The 3D has several effects:


increasing piece movement options
different board shape reduces flat move options for many pieces
perception of good versus bad moves is more difficult
occasional adjustment of board results in different dynamic (small boards are mobile)


this al means a direct comparison is difficult as the needed strategies change.

3D tic tac toe, however, merely gets more move options - the same strategies apply.
 So it varies by how the 3D is done.