The thing that's tough for me with this i.... Brady was without doubt the most successful QB of his era. If that's our definition of greatest, ok. But for the type of question we're considering about relative contributions, I think we're focusing on the merits of the individual player and coach and how they would apply to any situation including this one. How would Brady do without BB, how would BB do without Brady, etc.
Is Brady the most successful QB of his era if he played for, say, the Chargers and Rivers was drafted by the Patriots? I think that is far from a statement anyone should think they can confidently say yes to. In fact I'd probably pick the Patriots to have more wins and championships than a Brady-led Chargers. I'm not sure I'd pick Brady's Chargers to do better than the Colts even. Though Brady would still be elite, I do not think we'd see anything near to the Patriots run.
Another thought experiment. It's the start of the Patriots run. You have to either replace BB with a randomly selected current NFL coach... or you have to replace Brady with a randomly selected NFL starting QB.
I don't know about you, but I keep BB and roll the dice at QB. And I don't need to think about it much. I trust BB to put together a consistently great team with even mediocre QBs. Brady is a franchise QB definitely, but BB doesn't need an elite franchise QB. But then if he finds one... you get a run like the Patriots actually had. I don't think Brady is guaranteed even having all winning seasons if he has poorer rosters or coaching (like some of Brees and Rodgers recent seasons). He'll probably win a couple SBs when he's in a stretch with a good team and some luck. I don't think he pulls out so many close wins though without the contribution of Belichick's level of preparation he has his teams at.
I voted 60% for BB, but I was thinking 65. In retrospect I'd go 70.