I really don't think money is going to determine if Bryce stays in DC or not. He's going to get an offer from the Nationals that is at the least really close to the other offers (relatively speaking when you're talking about a 400 million dollar deal). I tend to think that if Bryce really wants to stay in DC, he'll sign an extension this winter. Otherwise, all next season will be full of hype about where he's going to land and for how much.
Maybe I'm naive to think so, but I don't see Bryce picking one team because they offer an extra 1 or 2 mill a year, which amounts to sofa loose change to him. He's already so well known and marketed, I don't think he needs to pick a bigger market just for that reason alone. I think it's a matter of where he wants to play and where his wife and him want to live, period. He seems to like being a National and there is a core around him that can win for years to come. He knows Rizzo is capable of retooling the team season to season and remain competitive.
I think another factor is if he does have an opt-out after 3 or 4 years. That means he could still hit free agency again before 30 if he wants. I think that helps his chances of staying in DC for now. He'd still be able to live out a dream of playing elsewhere later in his career.