I think people like Peyton because his "aw shucks" persona plays really well in the Flyover states. And, as others have pointed out, he's not threatening because he sucks big time when all the chips are on the table. Let's face it, most people can relate to that. Most folks aren't roaring, kick-ass successes in their professional lives...in fact, most folks just struggle to hold a job and make ends meet. Peyton comes from privilege and he's no doubt quite wealthy, but somehow people don't think he's in their face about it.
Brady on the other hand is married to one of the few people on the planet who is known globally by their first name and who happens to make 50 or so million US dollars a year doing so. He's also never tried to cultivate an "everyman" image...come on, let's face it, he left that behind when he was photographed carrying the goat or lamb or whatever barnyard animal that was and, while it might be great footwear, UGG is hardly the choice of most NFL fans. TB has been photographed on more red carpets with Gisele than Peyton has ever even seen. I live in NYC and scarcely a week goes by without a paparazzi shot of Gisele in the tabloids...there was one just this morning. I'm not saying Brady's not a great guy, a loving dad and a good husband and he is certainly a hard worker and a great teammate...he's just never pandered to the average, middle-class guy as effectively as Peyton has.
Belichick goes out of his way to be obnoxious. Let's fact it, it's why many of us love him and why his players will run through brick walls for him. But he ain't gonna win many popularity contests...nor would he want to.
And the team itself? One of the hardest things for me to accept after I moved to New York and the Patriots became successful was that I had to appreciate why Yankees' fans always seemed to love it when I told them that, as a long time Red Sox fan, I hated their team. They seemed to feed off the hate and want me to "bring it on" because they knew they were winners and, until a few years ago, we were losers.
It's very difficult for a team or a sports figure that wins consistently to also be "loved."
I'm old enough to remember that Jack Nicklaus, whom we all kind of "love" now, was actually resented and disliked when he was knocking the beloved "Arnie" off his throne back in the day. Whenever Watson or someone else had a chance to beat him, the fans were usually pulling for him...and more often than not, ended up being disappointed. It was only towards the end of his PGA career that people warmed up to Jack.