Talking strictly popularity wise - who was the biggest personality in the world at the time they fought? All 3 of them where culture phenomena. Is it even fair to compare people to Ali in this regard?
Dempsey was huge in the US and perhaps in other English speaking countries. However, keep in mind that in Dempsey's day, there was no TV or Internet. Most people did not have access to fight films. The average person would not have seen footage of Dempsey fight in the 1920's unless they went to a fight collector or someone like that. Most people outside the US would have read about Dempsey but very few would have seen him. So while Dempsey's name would be familiar to much of the world, most people wouldn't have seen him fight due to limited number of copies of the films/videos. Ali fought during an era where majority of people either had a TV or had neighbours or friends who had TV's. Many people in the 60's and 70's had watched clips of him fight. The news was much more international in the 60s and 70s and news went around much quicker than earlier eras. Ali-Foreman alone was watched by hundreds of millions world wide, possibly up to a billion people watched it live in TV. I don't think nearly as many people would have seen Dempsey fight. Tyson was great too but he was a phenom for 5-6 years while Ali generated massive publicity for 15 + years. So yes, while Dempsey was a well known name throughout the world and massive particularly in the US, he simply could not get the global exposure that Ali did due to no TV's at the time.
Ali in the 70's, especially post Zaire. He was perhaps the first truly global sports star. Tyson not far behind, though. Dempsey, as said, was before the TV era, so just couldn't get that reach. Tyson on the other hand has perhaps become even more famous as time has passed, with social media and all the platforms available today. But I think Alis ability to go to any place in the world and just make it stop hasn't been rivalled by any other athlete.
Dempsey was bringing in one hundred thousand people for some of his fights so it's between him and Ali. Tyson although very popular brought in soooo many casuals.
They are although Ali bought in just as many casuals as Tyson did, if not more. Its just that Tyson bought back the casuals that had left post Ali.
For modern cultural impact, I'd say a tie between Ali and Tyson. Look how much money a 59 year old Tyson vs Jake Paul fight generated, which is amazing considering that Tyson’s prime was the late 1980s
Many millenials who were born during Tyson’s first reign or gen z'ers who were born around the time Tyson fought Holyfield or Botha still know who Mike Tyson is, not to mention all the boomers and gen X'ers who were around while Mike Tyson was an up and coming young contender.
Ali was the biggest as a human being. Tyson and Dempsey were bigger as boxers. If you polled people in 1926 and 2026 and asked them to name a boxer any boxer a majority would name Dempsey and Tyson.