He wrote a great article in the NY Post last year before our playoff loss to the Jets, detailing why he's had success vs Belichick throughout his head coaching career and what his gameplans were like against the Pats. He was also pretty good on TV, breaking down the matchups and making his picks. He did pick the Jets to upset us last year FWIW.
He said Belichick's #1 goal is to not lose the game -- don't beat yourself. He also said that BB has his teams prepared for everything, so you have to throw something at them that they've never seen on tape before. He said the most important thing on defense is disguise because if you declare too early and tip your hand, Brady will pick you apart.
The article he wrote for the Post was about how the Jets could beat NE. It's a pretty good read:
NY Post - Mangini: Here's How The Jets Can Take Down The Patriots