Against pawns on opposite wings, the bishop controls one promotion square from afar while the king hunts the other pawn. The bishop's long range makes this possible; a knight could not do it.
This drill shows why bishops cope well with pawns on both wings. Black has pawns on a5 and h5, far apart, and the black king is nowhere near either of them. A knight would be helpless, but the bishop covers one side from a distance while the king walks to the other.