This fight almost took place in 1904 when it would have been a bit like Holyfield Bowe IV taking place today: The Fitzsimmons-Corbett match has aroused great interest throughout the country. It is the outcome of much talking on the part of both fighters. The coming meeting will be the second time the veterans have faced each other in the fistic arena. Fitzsimmons was the first man to score a KO against Corbett. This happened when he whipped him for the championship at Carson City, Nevada (March 1897). It should be a great fight as there is no love lost between "Gentleman Jim" and "Lanky Bob." Corbett has not forgotten Carson City, and Fitz says that Jim will prove "easy meat." The Plattsburgh Republican, January 2, 1904, p. 3 Lets say however that the rematch had taken place while Fitzsimmons was champion. Would lanky Bob have repeated the trick or would Corbett have become the first two time champion?
Corbett was too far removed from his prime at this point. With a few steps of his blazing reflexes lost and his legs starting to age, Fitz's economical style would get to him sooner. Fitz by KO.
Since Fitzsimmons was the champion he would choose the rules. I assume he would want the longest fight possible.
Fight to the finish rules, then. Corbett at his best went 61 rounds with Jackson, who was a boxer-puncher. Nevertheless, Fitz drags him into a long counter-fest, Corbett lacks some of the confidence of his last encounter and stays away more, and Fitzsimmons nails him in the later rounds (20 or so).
Corbett ,immediately after he had recovered his wind and was being consoled by his corner,"Youve got to fight me again, youve got to" Fitz,"not likely you gave me a bloody good licking". Corbett," if you dont fight me ,I'll lick you whenever I see you on the street". Fitz ,"Jim, if you ever lay a hand on me outside the ring,I'll kill you!"
http://query.nytimes.com/mem/archive-free/pdf?res=9A0CE5DD1638E733A25757C2A9659C94669ED7CF here is their encounter and Fitz' response a little while later and not in the heat of the moment. In reality, fitz peaked with this performance, and (like Johnson and later Ali) his career after his peak shows just what a phenomenal fighter he was, even though he was not prime in this stage of his career.
Corbett just wasn't there even leading up to their first fight. He was faded and it took a lot to really get him fired up. Fitz would beat him again, and probably with less hassle I imagine.