I think Belichick is the clear-cut GOAT coach, and Brady is the arguable GOAT QB (I'd take him over anyone who's ever played). Both have benefited from their career coinciding with the other, but Bill is the more important of the two by a nose.
He is the greatest coach in the history of American team sports. Baseball isn't the kind of sport where a coach/manager can have that much of an impact, Pop, Jackson and Riley all have some minor holes in their resumes that IMO exceed anything that can be detracted from BB for Spygate, and I don't know anything about hockey.
But let's face it. What he's done year in and year out, constantly adapting to every situation... just ridiculous. Another coach trying to prepare his team against a Belichick-led team must be a nightmare.