The secret to the Pats' success was the entire team. That huge O line, the D, and Brady in his prime as the centerpiece, the proverbial straw that stirs the drink. He wasn't a one man show, he had a great team around him.
Now that he's getting old, he relies on that team more than ever, and that team is now aging just like him. But put him somewhere else - like the Chargers or the Dolphins - and we will see a different Brady. If he's going to stick around and overstay he should also stay with the Pats, because he will definitely be showing his age once he's removed from that setting.