What killed Carroll with the pats was Bobby Grier overruling him on player discipline. He was a rah rah players coach who like Rex followed a hard ass coach. he treated the players as men and instead the team refused to police themselves.
When he went to Seattle he got the final authority on all thing relating to personnel. He no longer has to worry about the FO backing him. I am sure he has learned that a large percentage of football players are like over aged frat boys, that need to be directed and can not be trusted on their own.
The guy is a nice person also. (or I should say he projects that persona)