Found a quote attributed to Joe online “Jack Dempsey was the greatest fighter that ever lived. I always have thought so. I never saw Jack fight but I saw the movies of his fights with Gene Tunney and Jess Willard. That Dempsey was a great fighter, a great puncher. He just kept coming at you all the time. Hype Igoe, the old sports writer, used to tell me I could have beaten Dempsey because I had a better jab and could keep my balance better. This is the kind of fight I would have liked to get paid for but not fought. We'd have made a lot of money.' - Joe Louis
I think Louis stops Dempsey after some shaky moments, perhaps getting floored and hurt. But I wouldn't bet too much money on either.
If you are looking at all fighters from the first half of the 20th century, Dempsey is certainly one of the more impressive ones on film which is remarkable since a lot of his best fights weren't even filmed.
This would have been a pretty uncontroversial choice when Louis said it in 1964. At the time, the majority of people who weren't picking Louis himself would have been picking Dempsey (though Nat Fleischer was still keeping faith with Jack Johnson).