Let me preface this by saying Dan Marino is my favorite football player of all time, I usually think Joe Montana is the greatest, and I also like Tom Brady a lot.
Objectively, I think people fail to acknowledge context when judging QBs against each other, and I think it's pretty much a fool's game to compare different era and different contexts in a team game - especially football, the most fundamentally "team" sport of all major American sports, where the parts work in service to the whole and only like 5 positions get glory because the public is too stupid to process the complexity of the sport.
I really, really fukk with Tom Brady. At the same time, the popular narrative for Brady and Beli is an old one that hasn't been amended to be in step with reality. Beli is a genius, Brady is the greatest, and that's the end of story. Except Beli and Brady keep losing home games and big games on neutral turf when they are favored to win by a touchdown or more. And Brady has been outplayed by Flacco twice, Eli twice, even Mark Sanchez. Coughlin, Harbaugh, and Rex have out-planned and out-adjusted Beli on several occasions. And to the mainstream media, it's as if none of this has happened.
Your first paragraph explains the second one. People are lazy when heaping praise why would they be less lazy when doling out credit... The Pats should not have been favored in half those games, the softness of the AFC East has protected them for 4 straight seasons.
But to be fair, if you use the exact same context you're talking about then you know there's a lot that goes into explaining why one guy outplayed the other. Imagine if that was Brady on the Ravens going against that Pats defense. Injuries, etc. But Bellicheck talked to Harbaugh after the game and told him that he out coached him , etc., and all the superlatives.
But Bellicheck not being criticized is what I agree with the most. From the way he has built these stupid bend, but don't break defenses that have ruined cornerbacks (Sterling Moore admitted that on the Pats the DB coach told them not to turn and look for the ball) and mishandling of veterans like Seymour and Asante who they haven't been able to replace. To just straight up being unable to generate any pressure on QBs for 6 postseasons. All starting with his defense giving up over 30 to the Colts in the second half in 06. Everything since then has been trying to use these piecemeal strategies to get by. Over relying on Brady and thinking that they are smarter than everybody. Forgetting that at some point, talent will beat lesser talent if it is coached up (which explains every recent playoff loss).
He ran into coaches with teams as talented (and usually more talented in key positions) than his and couldn't get by on outsmarting everyone. He didn't make the changes he needed to because he's surrounded by a brain trust and has not had an outside influence or energy bring a new life to his team. It's no surprise that the Pats haven't won anything since Crennel and Weis left. Bellicheck thought they could do it all internally and never brought in anyone from the outside. What you get is stability, and winning as long as your hall of fame QB is still there, but a team that struggles to score in key spots and can't stop anyone in key spots either. And it's not that he didn't notice it, the Pats just failed on WR they drafted.
The guy who could "confuse any QB" with preparation has not done it in 6 years. Bellicheck crafted a vanilla team that is the antithesis of the sqauds that won SBs.