That would point to there being no advantage in perfect play. However, in imperfect play, the first or second player could still have a measured advantage.
There is no disadvantage to going second... in fact, in tournament games, the player to go second (white) wins about 2% more often than black does. All of black's first moves actually transpose, so white has the first real choice in the game, and also usually has the last move in the game, which can be an advantage.
If you consider that in the early game you want to keep low your number of pieces (because it keeps the number of possible moves high), it becomes somewhat obvious that going second is not a disadvantage at all.
