Plain chess -- 2-D, 3-D, or otherwise -- is a rule driven mathematical game. In a straight up match with no Games Theory modifications, Brainiac may have the advantage for logical maneuvers and forward planning, but Luthor would take it for intuition at times. Lex might have the slight advantage given they both operate pretty much at the same level to begin with.
If Games Theory is allowed, then Brainiac can have the advantage since Luthor is vulnerable to emotional manipulation and fatigue while Brainiac isn't.
Given all the above, I'd say overall, Luthor may win some early matches, but Brainiac can keep it up far longer and win more over the long run, intuition or not on Lex's side.
Out of ten matches:
Luthor/Brainiac - 6/10
Out of 100 matches:
Luthor/Brainiac - 20/80
IMHO
