Actually I think Doug was stricter than Bill B. Plus Bill B has the Super Bowl rings to back it up.
Doug wasn't a bad coach but it was his arrogant attitude that rubbed me the wrong way, even via NFL standards. Reports came out of him being nasty to secretaries, miserable, a control freak, and I believe he thought he was going to get the Jets job so he bailed. There's a reason why his face wasn't included once in the 2014 Bills highlight video.
I admit Rex who is Doug's opposite wasn't any better with his approach. Still I personally don't miss Doug.