There are less problems with Jeffries title reign, and with his pre title run. Dempsey resume has less missing in terms of the styles and sizes of men he defeated, but I still have to say Jeffries.
Are you ****ing serious? Jefries had only 22 crappy fights and the 90% were smws and lhws. Dempsey ranks higher and it is not even close
Ask anyone in the streets of your town who is/was Jim Jeffries and you will get a blank stare. Ask the same people who Dempsey was and 80% would say "a boxer" or whatever....in other words they would have some inkling of who he was. There are very few athletes with as high a recognition rate nearly 100 yrs after he won a title. The question wasn't "who wins H2H" (and that would be Dempsey anyway) but who would be rated "higher". I'm seriously tired of this recent Jeffries mania. He was an oaf in the ring, strong, yes, but an oaf. Dude got cut to ribbons by and old KWH (Fitz). An embarrassment.
"There are few athletes with as high a recognition rate" Interesting argument. I am also on a movie board. I remember a discussion a while back on whether Jayne Mansfield has more name recognition today than an actress like Deborah Kerr. The consensus is she probably does. So to cut to the chase, name recognition rewards celebrity, not necessarily accomplishment. Mansfield didn't have anything like the movie career Kerr had. She wasn't in the same league as an actress. But she was a rather over-the-top sex symbol who led a tabloid life and died young in a gruesome accident. All that might trump a solid professional such as Kerr in public memory. There have been famous celebrities who really did nothing much. I'm sure you can think of an example. When I was very young, I knew for some reason who Sullivan and Dempsey were, but I had no idea who Johnson and Jeffries were. Johnson has since become a historical celebrity in the last 50 years or so, but back then nobody much talked about him. I remember in the fifties being surprised on a boxing panel show when the three boxing experts on the panel all picked Johnson and Jeffries as the two best there had been. I had to look them up in the World Book at school the next week. So my bottom line is I don't think who is still known to the man in the street is any gauge of historical achievement. "Dude got cut to ribbons by an old KWH (Fitz)." I admit I am stumped about what KWH stands for. As for the argument, Jeff won the fight by KO despite the cuts, and Dempsey was KO'd in one by an old Jim Flynn who was never the fighter that the triple champion Fitz was.
I go with Jeffries. He fought a good cross section of the best, both black and white, up to 1903 or so. He should be scored for ducking Johnson in 1904, but otherwise had a strong career, and worthy title reign, compared to the other old champions. His only loss came at 35 and after a six year layoff to Johnson. I think Johnson better than anyone Dempsey fought. Dempsey not fighting Wills and Greb, and losing to Tunney, really makes it difficult for me to put him high among the elite heavyweights, despite his fame. on Jeff only having something like 23 fights. Two points. He might have had more. There is a newspaper report that he did. More importantly, his percentage of tough fights is very high, and the total number of tough fights not that different from most other champions. Jeff's record just doesn't have much padding. Using Matt's pre-Ring Magazine ratings, Jeff fought 16 fights against 11 men who appear in these ratings, mostly near the top. This doesn't include name fighters of the time like Henry Baker, Pete Everett, and Jack Munroe. It comes out to about 20 of the 23 fights were against name opposition. 20 such bouts matches quite a few ATG claimants, although certainly not those with outstanding longevity such as Johnson, Louis, Ali, and Wlad.
Jeffries was routinely viewed as #1, #2, or #3 by lots of historians until the 1960's, including the McCallum survey where he came out #1 from a group of 12 historians, which included Nat Fleischer. Once the people who saw Jeffries or had first-hand testimonials about him died out, the lack of film on Jeffries made him harder to know. The one film boxing fans have seen when he was washed up. If there was only one film of Ali and it was vs Holmes, his legacy would suffer 50 years after he retired too. Dempsey's legacy remains preserved, thanks to the several films, but when I look at it, his defense, and ability to take a punch look a bit suspect, but I have no doubts about his power and speed, which are excellent. I think Jeffries was better overall as he beat a better class of opponents, and also matches up better head to head in fantasy fights as he's one of the few old-timers with legitimate size, durability and athleticism.
Neither make my top 10, you can make a good case for both of getting into the first half of it without having to make much of an argument to someone who's schooled well enough on the heavyweight division.
I guess I need to do the obvious breakdown here: Title reigns Jeffries held the title for just under six years, and defended it eight times. Dempsey held the title for just over seven years, and defended it successfully five times. Edge Jeffries Pre title runs Jeffries won the title in about fourteen professional fights, and was undefeated during this period. Dempsey had a lot more ring experience during his pre title run, and a lot more losses. It would be fair to say that Dempsey beat better qualified opposition during this period, even though he was not thrown to the wolves as early. Edge, depends on your criteria Significant omissions The only major contenders that Jeffries failed to meet were Kid McCoy, Denver Ed Martin and Jack Johnson. I do not think that McCoy or Martin were particularly outstanding contenders, and Johnson was only an outstanding contender for the last year of Jeffries reign. Dempsey failed to meet Harry Wills, who was the outstanding contender for most of his title reign. He also failed to meet Harry Greb who was a better contender than many of the men who he defended his title against. Edge Jeffries Significant losses Jeffries only career loss was to the all time great Jack Johnson, in his final professional fight. Dempsey also lost at the end of his career, to a very fine champion in Gene Tunney, but he also has a number of losses in the period before he held the title. Edge Jeffries Size and styles of opposition It would be fair to say that Jeffries challengers were better qualified, but you could argue that they were smaller, and less stylistically diverse. Dempsey met everything from small technicians, to super heavyweigths, boxer punchers, and sluggers. Edge Dempsey Historical impact Jeffries raised the bar significantly over his predecessors, in terms of frequency and quality of title defenses, so you could argue that he set the template for the champions who followed. Dempsey however raised the global profile of the sport, and ushered in the era of million dollar matches, becoming a global icon. Edge Dempsey Conclusion Given the phrasing of the OP, I am going to treat it as a clinical analysis of who was the better champion, as opposed to the greater sporting icon. On that basis I have to call it for Jeffries