Your logic and that of 71% of the respondents is flawed.
Belichick is a great coach.
Brady is a great QB.
You don't get great coaches WITHOUT great QBs & you don't get dynasties without them either. The question asked is who is more responsible for the dynasty. The answer is obvious, Brady. Without him the pats are just another team with an eccentric HC. With him they are a dynasty. Toss in the fact that he has never held their feet to the fire monetarily and that he has publicly put up with 99% of Bill's crap and you have the NE dynasty.
Put Rogers in that situation and tell me what happens.