I think a huge part of this team looking so much more potent on offense is generally the change in attitude of the coaching.
Parcells played games not to lose. Keep your cards close to your vest. Lot's of running for ball controll. Defensively he didn't gamble with exotic blitz packages as much. It had been mentioned on here many times before, but Parcells favored his players winning individual matchups as his strategy for success.
When you look at the way Wade Phillips coaches defense as opposed to Parcells, you can see how it also affects their offensive decisions. Parcells would gamble on 4th down. But if we had a lead, he would protect it, rather than take shots downfield, etc. I think the offense is just opened up more in certain situations.