Sullivan would win. Sullivan is most important boxer ever. His fame during his time basically created the sports pages in America. He was front page news. No other athlete dominated the news like him. He dined with the President a first for an Irish man. He went a long way in getting the Irish accepted in America much like Joe Louis and later Jackie Robinson did for black athletes. He’s a monumental character in the sport.
The point should be made that men like Jem Belcher, Tom Cribb, Jem Mace, and John L Sullivan were huge sports stars in their own right.
A bare knuckle fighter would have a low work rate, but the Queensbury bouts of that era were usually scheduled for 4-10 rounds, which might have resulted in a high work rate.
I think placing Sullivan with the other QB champions is a mistake. Sullivan is maybe the greatest bare knuckle champion of all time. As a QB champion I do not even rate him. He has a career we call QB today but was really mostly mixed rules. He has a resume consisting exclusively of men who were LPRR fighters asked to fight under new rules. His fame allowed his draws to be handled like wins. Y'all can't even define a match or moment when he actually won the title almost like as if Sullivan became champion on popularity alone. Nutrition to this man is a pint.