I have a slightly different take; I think what they both want more than anything is to win a SB without the other. Belichick of course, can outlast Brady and I think he will for that reason. Of course, now that he's lost Jimmy G he needs to find a QB. I wouldn't put it out of the question for him to pick a veteran.
I've always thought it a very remote chance Brady ever plays anywhere else; it would take a situation like Manning had in Denver -- a team that had everything but the QB. I don't see that currently in the NFL. Even with all his arrogance, Brady realizes how valuable Belichick has been in winning all those Super Bowls and he isn't going to find that anywhere else. He sure as hell isn't going to some dumpster fire team like Jacksonville or Washington.
I still think he plays in NE next year, but retirement is the only other legit option at this point.