The way I see it, there are basically two broad models for building a championship team out there right now: One is the Walsh/Gibbs, ultimately Don Coryell model that is sometimes called the "West Coast offense," but to me means any team that relies on the passing game primarily on offense and uses short passes to establish ball control; these teams usually play a style of defense that isn't meant to suffocate the other team as much as make enough big plays over the course of the game that the opponent can't keep up with the efficiency of the offense. The other I'll call a Parcells/Belichick, ultimately Chuck Noll model which is thought of as the "old school" or "conservative" approach, establishing the running game, controlling the clock, and making the opponent work hard for every first down defensively.
Every once in a while, a team has a single unit or overall talent that is just so overwhelming that they win without using one of these philosophies, say the '00 Rams, the '85 Bears and '01 Ravens are examples of dominant units, while the Cowboys of the '90's just had more talent than everyone else, particularly that massive o-line. But otherwise, all the champions had one of the two models, as I see it.
San Francisco '81, '84, '88-'89, '94
Washington '82, '87, '91
Green Bay '96
New Orleans '09
Green Bay '10
New York '86, '90, '07, '11
New England '01, '03-'04
Tampa Bay '02
Pittsburgh '05, '08
It seems like the Walsh model was dominant in the '90's, I think there are probably a lot of factors that led to that, but the biggest may have been the short supply of good quarterbacking. Teams that had good QB's and could run that system were at a huge advantage. In the '00's, the Noll model made a big comeback.
One team that I think is interesting considering this theory is New England. Early in the last decade, when they established their dynasty, they played a low-turnover, ball-control style and had a great defense. Then their personnel changed and Brady developed into an exceptional passer, so to Belichick's credit, he decided to adapt to playing more of a West Coast style, with spread formations, short passes, etc. You don't see coaches switch gears like that too often.
The league's rule changes also necessitate more focus on the passing game.
The Giants are an interesting case also because their coach favors the Noll-Parcells model, but the GM responsible for building the roster expoused an "offense wins championships" philosophy that was closer to the Walsh model.
The Giants seem in good position now to make the kind of switch the Patriots did mid-decade. I think a lot of the struggles we see the team having right now may be a case of growing pains related to a roster built to pass, score and make big plays on defense and a coaching staff that wants to dominate up front and control the clock, etc. Funny thing is, when it all clicks, that struggle can create a team with a perfect balance of the two models, the Giants can get hot and go on these big tears. They were lucky to have a couple of them in the playoffs and win a couple Super Bowls, but if you think about it, almost every season in the past decade has had a five or six game winning streak at some point and some other really out-of-sync phases as well.
Anyway, glad this board exists so I can rattle on about my aimless NFL theories!