Yes, we can be pretty stacked on offense, but he would still be leaving a 12-4 team and going to an 8-8 team, so it's pretty hard to argue he would be putting himself in a better situation. Plus, winning isn't just about offense. The Patriots had the top defense in the NFL in 2019, and it's a safe bet they will be a much better defense than the Cowboys again in 2020. To go with that defense, if the Pats can add a TE and another strong WR to pair with Edelman, the offense can be back in business as well.
I doubt a guy with 6 Super Bowl wins, 4 Super Bowl MVPs and 3 NFL MVP's is worried about having not won a Super Bowl with 2 different teams. I can't imagine he feels he has fallen short of Peyton because Peyton did that, plus Brady isn't trying to be Payton - being Brady already goes beyond that. Besides, if he's looking at his legacy, a player who spends his entire career with one team is always perceived very favorably by fans and media.
The only chance of him leaving NE in my mind is if the Pats were to tell him he isn't guaranteed to be the starter, and I doubt that happens. What leaving NE by his own choice would do is cause some ill will with a fan base that idolizes him. Think about Roger Staubach leaving the Cowboys - while he would still be a fan favorite if he had left the Cowboys, some of the luster would have been lost because he would no longer be seen exclusively as a Cowboy. As for playing on "the big stage", how much more attention can Brady get or does he need?