All things being equal, I'd generally agree with your approach, opting to go with a hungry young coach over a retread. Problem is, that's been the Jets' MO since Woody Johnson took over as owner.
Each HC under Johnson has been a first-year HC from the defensive side of the ball: Al Groh, Herm Edwards, Eric Mangini, and Rex Ryan. Even going back to the pre-Woody era, we had a lot of first-time HCs. 2015 might be the time for a retread, as there really aren't any great upcoming candidates this time around.
If they were to bring Fox in, he'd be inheriting a pretty solid defense that is only a couple of pieces in the secondary away from being back to the elite status it had in Rex's early days in NY. He'd also be in heriting nearly $50 million in cap room that must be spent under the CBA's new spending rules, most of which could be focused on building a quality offense. The Jets also have a soft slate of opponents next year. All of that considered, if we bring in a veteran HC like Fox and use the cap space wisely, there's no reason that the Jets couldn't rebound and be a playoff team in 2015.
The roster was not nearly as bad as it was made out to be this past season, Rex and company just did a phenomenally poor job of coaching it and Idzik made the critical error of not shoring up the WR and CB positions. The rest of the roster, while not on the level of some of these current playoff teams (obviously) wasn't exactly the travesty that they were made out to be either.