For the intersection of fans who know the soccer world inside and out and area at least casual NFL fans, the comparison is easy - Bill Belichick is the Jose Mourinho of the NFL.
The guy everybody loves to see lose. A stubborn will to do things their way. A shared psychological tactic in the sense that they both think that the game is won by preying on opponent's mistakes rather than their own excellence. (Mourinho is famous for his "the team with the ball makes mistakes, and the team with the fewest mistakes wins games" philosophy and Belichick is notorious for deferring the kickoff) The cold demeanor that makes it so easy to love them as a fan, hate them as anybody else, and maybe most importantly, an insatiable desire to win.
They each have experienced complete dominance in their own ways. Jose has won the league in every country he's been to and won the treble with Inter in 2010. Belichick has been a near constant in AFC Championship game and been to the super bowl for what feels like every year of my life.
The difference, and the problem, is they coach very different games. It's much harder to deny Belichick's greatness than Mourinho's. The NFL, and American football, is all about winning. Soccer is a much more romantic game.
Johann Cruyff may not have been the first to say it, but he was well known for wanting to play in a way that makes fans want to show up to the games. He has passed down this philosophy to his disciple, Pep Guardiola, now known to have a fierce rivalry with Mourinho, each modeling an opposite approach to the game.
It is much easier for the soccer world to dismiss Mourinho because when he doesn't win, he has nothing to fall back on. Guardiola does. Even if he loses, he has a beautiful vision of how the game should be played. I'm not an NFL tactician but I do know that Belichick favors the passing game because it works to his strength(s) namely Tom Brady. But are there "beautiful" and "ugly" ways to play football as there is to play soccer? I'm admittedly not much of an expert in the NFL but I can comfortably answer no. There is, with some basic exceptions, one way to play football - win.
Bill Belichick has become an expert in winning, which means he doesn't have to answer to anybody about anything. Mourinho is an expert in winning too. But if there is a lapse, just for a fraction of a season (far less time than any NFL coach is given) the manager is out, and the past winning (often) means nothing.
This is not true in the NFL. Any coach that wins a super bowl buys themselves a huge buffer zone. Why? Because they won. What else is there?
This is an honest question to anybody who knows both sports: does the obsession with winning at all costs hurt or harm American sports? Is it better to have a driving philosophy other than winning all the time?
Does it make you better, make you win more, make you become the best, like Belichick?
Does the lack of an appreciation for a style, a system, a beautiful way of playing the game destroy whatever you've done in the past the minute you stop winning, like Mourinho?