According to webster, macho = Aggressively proud of one's masculinity.
Byronic= "a man proud, moody, cynical, with defiance on his brow, and misery in his heart, a scorner of his kind, implacable in revenge, yet capable of deep and strong affection" or "an antihero of the highest order. He (or she) is typically rebellious, arrogant, anti-social or in exile, and darkly, enticingly romantic."
Which to me are kind of different personalities.