From what I have seen/read Russell Wilson's main difference with Pete Carroll is that the Seahawks don't wan't his input into how to run the offense. That was also one of Brady's main differences with BB. If BB didn't want Brady's input, I really don't think he is going wan't to get pointers from Wilson about what they should do.
Yeah, but Wilson's issue is that he feels they don't invest in the o-line and it is getting him killed. That wouldn't be an issue with the Pats because they typically make having a solid o-line a priority.
I still don't think there is any realistic chance that the Pats will trade for Wilson, but I am not sure he would have the same issues with the Patriots.