I think it is really harsh to say that Brady's 2 picks defines his stature behind Montana, even though no picks in 4 super bowls is mighty impressive.
Well first of all, Brady threw picks in multiple other Superbowls, so it's not just those two I am basing it on. His picks caused his team to lose in some cases. How can you ignore that?
Second... its more harsh to deny Montana when he outperformed Brady, right? We can't just like Brady more and really, really want Brady to be GOAT. When we are splitting hairs between Hall of fame players, we have to look at their performance, we can't just go with who we like better. Its harsh that SEA had to lose because of Wilson's 1 INT at the end, but that's football. Mistakes matter. That's how we judge between the best and the almost-best.
Montana is undefeated in Superbowls. Brady can't achieve that. Period. For me its open-and-shut, especially when Montana has the same number of SB wins and zero SB picks. There is simply no rational argument for Brady to be GOAT.
Something different about Brady's 4 rings--all of his Super Bowl wins were super close
But that just further bolsters why Montana is the clear winner. Brady struggled to win the SBs while Montana was blowing people out. And these weren't chumps Montana was stomping. We're talking Dan Marino and John Elway for goodness sake. Brady got his lunch handed to him by Eli Manning of all people... twice!
To me the more interesting question is where to place the Patriots dynasty (yeah, it's a dynasty people) in history
But, The fact that you have to argue that its a dynasty says a lot doesn't it? (I agree with you BTW

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In the Brady/Belichick era
the Pats have sat atop one of the absolute worst, most pathetic, inept, cakewalk divisions in football. That has played a huge role in why they have been so dominant. While the Steelers and Ravens (and now Bengals) kill each other all season and wear each other down all season, the Pats (and Colts) coast to easy victory after victory with relative minimal injuries or difficulties. That is a huge factor in why Brady and Manning have so many comeback wins... because they play so many games against powderpuff teams that can't close the deal.
Another significant factor about that terrible division (like the equally terrible AFC South) is that it is unfairly constructed, precisely to advantage Brady (and Manning... and now Luck). The Colts should obviously have been in the AFC North and the Ravens should obviously have been in the AFC East (Miami belongs in the South, with the other Florida teams, JAX is AFC South and Tampa is NFC South). An AFC East with the Ray Lewis-Ravens in it makes Brady's legacy much more interesting doesn't it?