I guess we just have a difference in opinion. I view a big play as demoralizing but I view being able to get consistent gains even more so, especially in the running game because the defense knows it is coming and can still do nothing as the offense slowly goes down the field.
I think I can draw out my argument like this:
Say the big play offense is the all-or-nothing risk, and say it's equivalent to the standard "consistent play", meaning in either case you'll win the same amount of games. You're just as good a team, it's just your choice of play.
If your team isn't stacked with talent, the difficult games (and this applies directly to our 2012 run) will require more than just your average output to win. That means the only way you could win is by being a risky offense and succeeding. The Patriots are the classic "methodical drive" team, and they've consistently beat weaker teams but haven't won the Super Bowl in a decade. That might be why.