I think the main difference was simply competent QB play. And maybe the addition of Teller & Foster. Other than that, it was the same coaches, same players.
What Barkley did was get the ball to the primary receiver, and in such a way that they got separation and YAC. Take that first long pass. Peterman & Allen would usually be holding the ball too long then dumping it off to the third option. Or in Allen's case, taking off running.
What we saw with Barkley was execution of the plays as Daboll intended and when that happens, the O hums. And, BTW, the Jets D is not awful. The O output wasn't because they stink, but because the Bills have decent players who were able to show that simply because they got competent QB play for the first time this year.