Sherman is a better player, but by how much?
If we sign McCourty for say $7M vs. Sherman for $11M + 1st/4th round picks required to trade for him, Sherman is a superior player still, but McCourty is the superior value. As we don't have a 1st, it's more than likely that would mean trading Butler at least.
So you can keep Butler and sign McCourty, or have Sherman for both of them basically.
I also hate the argument that Team X has cut this guy so that's pretty telling. Bad teams make bad decisions. Dion Lewis got cut by the Browns. And the Colts. Nobody wanted Edelman for more than the minimum when he was a free agent. The Eagles cut Chung. The Bucs cut Revis back in the day.
Just because a guy is cut by a worse team doesn't mean he can't be a good player for the Patriots.