Where would Peter Jackson have ranked relative to the heavyweight champions?

Some of the statements from contemporary writers suggest that Jackson died as much from a broken heart at never getting his well earned title shot as from TB..I didnt include them as that is unscientific conjecture.
Jackson was Sullivan and Corbett's nemesis,Sullivan getting past his best, took refuge behind the colour line.The Corbett Jackson fight was supposed to be an eliminator to determine Sulivan's next opponent, Sullivan quickly took up Corbett's challenge after his draw with Jackson, but neither he nor Corbett would go near the Virgin Islander .
Jackson would probably have beaten the fading Sullivan ,imo ,and he had proved himself the equal of Corbett ,even carrying an injury into their fight. His day was gone after Fitz stopped Corbett, he was retired and living a life not conducive to good health .Jackson had struck up a great friendship with Joe Choynsky ,when they toured in that racist play Uncle Tom's Cabin ,Jackson playing the title role . People forget how bigoted many people still were in the States, when Choynsky lost to Walcott he was castigated violently in the press , for " letting down his race" .In contrast the UK was a paradise for Jackson ,where he was treated as an equal and respected as a leading pugilist, ironically it was this that lead to his descent into drink .

 

And yet not every report was so sparkling.
One or two questioned his ability to take punishment to the body and at least one other seemed to think he was a stiff puncher, but nothing special in that department. Actually, that was noted more than once.

Regardless, if given the chance Corbett got against John L, I'm fairly certain he would have beaten the dissipated Sullivan by that point, probably in an easier fashion than Corbett managed.
How he would have fared from there is anyone's guess, although I don't think there were many fighters to seriously challenge him for a while...he was certainly blatantly ducked by Sullivan and was one of the best (if not the best) heavyweights of his era, but as noted above he seemed to fade rather quickly as a fighter.