I think how far McCarthy takes the Cowboys largely depends on if Jerry Jones is willing to take a couple more steps back and allow the coaches to coach without his meddling or needling comments.
Garrett wasn't a very good HC but it certainly didn't help having the owner publicly question his decisions and his game plans on a fairly frequent basis. Those comments from Jerry tend to influence game plan decisions. We don't need that.
If you hire a man to do a job, let the man do it. Especially when there's 25 years of evidence that shows your method doesn't work.
It's just my gut feeling, but I think that Jerry acts according to the accomplishments and temperament of his head coaches.
Meaning that with guys with skins on the wall and more dominating personalities, Jerry backs off a bit and gives them the leeway to do their jobs and lead the troops. I think that was the case with both Jimmy and Parcells.
Conversely, with the less accomplished 'just happy to be here' guys like Gailey, Campo, Phillips, and Garrett, Jerry's personality and talk came to the forefront more and he was 'the face of the organization'.
I expect that based on accomplishments and track record that McCarthy will be regarded more like Johnson and Parcells.
Again, just my opinion.