Pick your bets gentlemen. This is particularly interesting because both these gentlemen are title claimants.
While film on Sharkey is limited, he did a good job vs his class opposition in general. Bivins was defeated by 18 different fighters in 112 matches. This is a bit too much, and suggests Bivins has issues vs multiple styles. So who wins? Bivins was mostly a boxer type. His best assets were solid skills, and long arms. However, Bivins was a light puncher, and had questionable chin vs Punchers. Sharkey was a wild bull with stamina, power, and durability to spare. Sharkey's skills and tenacity was enough to catch up to the best boxer types of his generation. Shareky KO'd very quick Kid McCoy, and got the better of Corbett. Best guess is Shareky's power and relentless style is too much for Bivins. Shakrey via mid round TKO would be my best guess.
Sharkey, for reasons Mendoza has outlined. I wold just like to add that I don't think we saw anything like Bivins best up at HW. If things had been a little different for him, he might have been a reasonable pick here. But things being what they were, I see Sharkey as a surity to stop Bivins.
I think Bivins is underrated here. He fought, as best as I can tell, 75 fights against opponents who were rated by Ring Magazine at one time or another. He won about 50. He won 25 fights against opponents who were rated when he fought them. Only perhaps Langford of non-champions fought such tough competition. And he did not do that badly. He won 86 of 112 fights to Sharkey's 40 of 53, 77% to 75%. Bivins' chin has been questioned, but he was only stopped 5 times in 112 fights, or about 1 time every 22 fights. Sharkey was stopped 3 times in 53 fights or 1 every 18 fights, and Sharkey should have an extra KO defeat on his record from the first Fitzsimmons fight. Bivins was probably more durable. He was stopped only by Charles, Moore (3 times) and Lem Franklin. Sharkey was stopped by Fitz and Ruhlin (twice). I would give Sharkey the edge as a puncher, but his record is padded with knockouts of men who were pretty much unknowns. He did stop Choynski, Ruhlin, McCoy, and old Goddard, but that list is no more impressive than Bivins' list of Archie Moore, Lloyd Marshall, Clarence Henry and Coley Wallace. I like Bivins to outbox Sharkey easily and probably batter him into a late round knockout. He was a much better and more consistent fighter over a longer period of time and beat many more good men, as well as bigger men.