Sean Payton’s reputation among NFL fans

Sean Payton in Denver is equal to Jimmy Johnson in Miami. He was great in his previous position and will be good in his current.
That's a very big "if", IMHO. While Johnson didnt build Dolphins into a dynasty after Don Shula's retirement following the 1995 season, he drastically improved Miami's defense, which had always been a big problem under Shula since early 90's when they couldn't advance past the Divisional Round and why more talented, better depth teams always had Dolphins' number. Johnson drafted guys like Jason Taylor and improved the offensive line, and under JJ, Miami enjoyed three winning seasons with post-season berths and two seasons (1998 and 99) where they advanced to the Divisional Playoffs.

As you stated, if Johnson's tenure in Dallas in the early 90's could be classified as great or outstanding, his Dolphins' tenure was more along the lines of "good but capable of better". I think those late 90's Dolphins' teams had more then its fair share of untapped potential and unfortunately, during Johnson's tenure and especially with his successors, it got wasted because Miami became a second-rate team behind the now-ascendant Belicheck and Brady Patriots Dynasty. I also believe by the last few years of his NFL coaching career, Jimmy came to the realization that the game was passing him by and that he was going to be increasingly hard-pressed to survive or evolve in the newer, stranger world of 21st century NFL football and since his mother had developed health problems by 1999, he used the opportunity, plus Miami getting its arses collectively walloped by Jaguars, 72-10, to retire for good and become a popular, NFL pre-game studio talking head.

The jury is still very much out on how Payton will be able to turn Denver into contenders because he's the HC of a decent team that is same division as the new Dynasty team, Patrick Mahomes/Andy Reid Kansas City Chiefs--a team that will continue to be very good for the foreseeable future even when Reid finally retires. Kansas City will be remembered probably as being the most dominant, unbeatable team in the 2020's as Patriots were during the 2000's and 2010's. This is "their time" and even if Chiefs don't make it, other AFC contenders like Baltimore, and perhaps Buffalo and Cincinnati will be close behind taking their place.