It's both. Also I don't think you are giving enough credit to the organizational structure as a whole. In NE you don;t have a meddling owner who wants to be coach and GM (see Dallas). They hire people to do their job and if they don;t do said job, they are gone. Belichek was a defensive wiz for a long time, but even they could see that after a while he could not just take any castoff and make them a star. It still happens occasionally but not nearly as often as it did in the past, especially on defense. They also manage their roster better than anyone. They understood that defense became difficult to play at a high level and went more to the offense (helped to have Brady).
With all that said there is one thing that Belichek still does. On a weekly basis, he changes up what his own team does to counteract his opponent's strengths. I understand the "do what we do" mantra and not worry about them, but there is nothing more awesome to watch than to see a team taken out of what they do best b/c the opponent took them away. Way too many coached teams in many sports on many levels look the exact same every game Wash, Rinse, Repeat.
