I think the final question has more moving parts that that. The culture each guy wants to build and how he gets there is a massive consideration. Bill was "Do your job. I am the brain." That worked for him. It even had potential to work over his last 4 years if he hired an actual coaching staff rather than using Judge and Matty P. Needless to say Bill failed the draft too many times to build a winning team. I think the culture by the end of his tenure was not sustainable with modern players.
On problem with Mayo was that he swung the pendulum too far in the opposite direction. He wanted to be the players friend. This is what people do in relationships. They seek the total opposite and it typically fails. Mayo called his team soft, and they were because Mayo is soft. He had poor discipline, structure, and communication. He acted like a bumbling fool on Sundays and had to fix it on Mondays. The way his players mouthed off was ridiculous towards the end. White, Tavai, the WRs, Godchaux.. The team gave up 147 rushing yards to the Chargers and Godchaux said they had a good game. How blind and stupid can you be? If you want to see a telling sign, watch Gonzo's presser yesterday. He was grinning the whole time talking about Mayo's firing. Granted, he is a quiet and happy type of guy, but it looked like more than that to me.
So here it is: What culture does Vrabel or BJ bring to the table?
Vrabel: He knows what is expected in the building. He was one of the hardest working players who knows "The Patriot Way" and can bring back the mentality if he walks through the front door. He is all abut hard work and discipline. That WR room is a whining mess. I would love to see him tell them to shut up and work. With all that comes a danger too. We do not want the next Bill who cannot relate to players. Brady and McD openly say Vrabel is an ahole. That can be good and bad. Vrabel has to have a dynamic OC to develop drake, and a total defensive scheme overhaul.
Johnson: He brings the modern offense, something this team has never seen. Every Pats fan wants to see Drake in that offense. The question is what would need to be done to get it to Detroit's level. A couple of draft picks isn't going to do it. 75% of the o-line needs to be replaced. The complete WR room with the exception of Boutte who is a 2-3 option needs to be replaced. What discipline and culture does Johnson bring to this team? We don't know and cannot assume its the same as Campbell. That dude is a unique personality and a beast. What Johnson is like is unknown.
You know what you are getting in Vrabel. That is the attraction for many.