Great coach or great QB?

The Patroits are on top of the NFL right now and look to stay there for the near future. They have the ingredients they need to stay on top; a good coaching staff, a good GM and a good QB. But which of those is the most important ingredient?
Bill Belichick wasn't such a genius before he got Brady, in fact, he was just another defensive coordinator who didn't get along with the media and was run out of Cleveland. He gets the job in New England, inherits a pretty good team and has it heading in the right direction. Then one Mo Lewis hit on Drew Bledsoe, and in comes Tom Brady a 6th rounder the Patriots didn't even want to draft, he was the best QB left on the board. Suddenly Belichick looks like a genius for playing Brady, and the Pats have one of the best QBs in the league fall into their laps.
Before Pats fans come yelling about it's more than luck Brady works hard etc. I'm not suggesting he doesn't, I'm not suggesting he's not a great QB or that he wouldn't be as good in another city. Although I do have a hard time picturing Brady being successful in Detroit, Arizona, Houston, Cleveland, New York those places seem to eat QBs. I am suggesting that karma has something to do with the right QB being paired with the right coach at the right time and that's what happened here.
It also happened when the Steelers took Terry Bradshaw, the Cowboys took Roger Staubach and Troy Aikman, the 49ers took Joe Montana. Interestingly, Bill Walsh also wanted a different QB when the 49ers took Montana, sometimes genius gets some luck.
My conclusion is that the situation has to be right for a team to succeed long-term, and the thing people often miss when they call someone lucky is that the player and the coach have to take advantage of the opportunity. That's what the most successful teams and players have done, they work and do not assume that the opportunity will be there again because chances are that it won't.