He would have made the call in the 20s or 30s, so he obviously had some balance between old dog and new dog in his rankings.
Hang on just a second. We know almost exactly what Tunney was, but we have a much less clear understanding of what Sullivan was.
I don't really rank Tunney as highly as many do. With that said, there is no way I can make a sensible pick in this fight. We have no footage at all of Sullivan. We have his record and what contemporaries said about him. I think we know that Sullivan was far down the hill from his peak years in the Corbett fight, so I doubt if there's much to be learned there.
Even then you had Jeffries, Fitzsimmons, Corbett, Sharkey, Ruhlin, Kilrain and earlier bare Knuckle fighters with a better heavyweight resume. Tunney must have had less than 10 fights at heavyweight. Gene was a brilliant light-heavyweight, but not a great heavyweight, in my opinion.
Djanders makes a good point that we have no Sullivan footage to refer to. So I'm just going to assume that Sullivan in general reflects his earlier era and that his skills are on par with that. We have seen some of Corbett, the guy that beat him. Sure, triangle theory doesn't always work out but I'd bet the house on Tunney sending Corbett out of the ring on a stretcher if they'd ever fought. Tunney we have seen and he looks quite modern and composed. He gave Dempsey all he could handle and he managed to compile a metronomically consistent record. He proved that he could handle a wide variety of styles. I think the circumstantial evidence is in Tunney's favour.
I don't think there's any case for rating Sharkey, Ruhlin or Kilrain ahead of Tunney at heavyweight. It's doubtful if any of that lot was ever even the second best heavyweight in the world at any point. You never really see rankings of fighters including pre-Sullivan fighters back then either. I don't think many had any real knowledge of them.
Sullivan acknowledged later in his life that his style was a thing of the past and that no version of himself would have been able to beat Corbett, so I doubt he would have much to offer Gene Tunney. He would still go the distance though, since he was infamous for his durability. I do think there's a chance that John L. could drop him with something weird early in the fight. He had such a bizarre way of striking that even boxers during his time were bewildered by it.
I can't imagine Sullivan was good at all, Corbett, by all reports, completely outboxed him and stopped him, Tunney is wayyyy better than Corbett. Sullivan was the start of boxing, and when a sport is only just started, it evolves very quickly and I can imagine how much more evolved Tunney was, Tunney actually looks quite modern in the way he fights