I don't think that White's first move advantage is a flow in
a game. Advantage of the field, or Home territory is a natural element of
every battle, including Chess. And I am not a big fan of creating 100%
symmetrical variants (a little symmetry, or system, would be nice
though.)
Personally, I think the only way to eliminate White's first move
advantage is the one used by the completely chaotic variant _Balanced_
Marseilles Chess, which is also applied to most double-move variants,
since the side to move is always half a move behind.
White moves one move, Black makes two, White makes two, and so on.
Progressive Chess also, following a similar principle, eliminates White's
first move advantage. (Though I am not sure if it gives him something in
return. I never played it.)
[[Derek Nalls published his comment while I was typing mine.]]