Rayleigh has been on the bottle for years, doing nothing but roaming the bars and kicking back.
Garp has been kicking ass, inhaling napalm each morning while biting on cannonballs and spitting out nails. And constantly patroling the seas. He's got his own, private "Garp-the-Hero" motive battleship and crew for crying out loud. Had he gotten serious, and I mean death-gaze, teeth-clunching serious into the fight it could have been bleak for Sakazuki.
To all we know Garp is a legend. Not inferior to Sengoku (only the rank divides them). He is the text book example of the old fart, who can kick the shit out you so hard even your children will feel the bruises.
Ultimately it is up to the author to decide as it isn't us who create the storyline, but based on what we know and what we ever learned form reading manga, Sakazuki would have his head on a stick by the end of the day.