IMO, Quinn is not the HC you want to turn a bad franchise around. He is competent from an Xs and Os perspective, but I wouldn't call him a defensive genius. He never had better than average talent on D for 6 years in Atlanta, and never delivered better than average results. And while the Cowboys players plainly love him, I wouldn't call him a "culture" guy. There was a stink of flop sweat for his last couple years in Atlanta that he never overcame... it was one underachieving 8-8 year after another, one coordinator firing after another, and he never came up with any answers.
He's in a good spot right now... he loves this Cowboys D, and they love him. But if you gave him a teardown job like say the Colts where he is starting with bare bones on defense. Or brought him into Denver and told him to turn around a team that already believes it's screwed for the next 2 or 3 seasons. I don't think he builds either one into winners.
His best coaching-carousel job is probably Carolina. There are some seriously talented pieces on that D like Jaycee Horn, Brian Burns, and Derrick Brown. And while the Panthers' management has been schizophrenic, the players aren't cashing it in yet. They fought hard after a horrible start.
The million-dollar question with that job is "who will my QB be". But if you ask Quinn to motivate a talented defense, and get them playing fast, aggressive ball like Dallas... I think he can do that.