The common opinion among grandmasters is that the advantage of the first move is not decisive in itself. Black is able, if he plays an error-free game, to counter any White threat. The initiative is only gained through the exploitation of an error by the other player.
Conceding a pawn, however, is enough to lose most games. Though many endings of king and pawn vs. king can be drawn, the superior forces can be maneuvered to remove these possibilities.
Of course, I blow these opportunities on a regular basis.