Pittsburgh's 3 Super Bowl appearances during the Brady era:
XL: Denver dispatched the Patriots (in Denver!), Steelers beat the Broncos the next week.
XLIII: Patriots were "Sir Not Appearing in this Picture" for the playoffs thanks to Bernard Pollard giving Brady a season-ending injury in Week One
XLV: Patriots lose to the "Sanchize" at home, Steelers pick off the Jets the next Week.
XLVII: Beat the Patriots in New England!!, as was their wont during the Flacco Era. Baltimore's biggest problem is that they couldn't beat other teams. Rock Paper Scissors is weird, dude.
Indy: Well-documented instances of consistently losing to the Patriots aside...
XLI: Kept their together in the early round of the playoffs and made the hard-won home field advantage pay off in a comeback win against the Patriots, for once. (This loss also marked the end of the "Brady as game manager" era in New England.)
XLIV: Patriots got Flacco'd
XLVIII: Broncos defense is good enough when they play New England in Denver
50: Ditto (barely) (As for why they couldn't do this more often, John Elway is a moron as an executive.)
Giants: Don't have to face the Patriots before the Super Bowl, spent much of this era otherwise underachieving or flailing around, Rock Paper Scissors is REALLY weird.
Gist is, there are two approaches to getting around Brady during this era.
1. Let somebody else take care of him.
2. Rely on rock paper scissors advantages and hope you don't run into somebody who has the same advantages on you.
Please note that both strategies rely heavily on luck.