I've always been under the impression that the offense has more of an advantage than usual in this situation. First of all, they have four downs to work with. That extra down makes it much easier to score. Second of all, the offense is able to play more aggressively, because they don't have to worry about what happens if they fail, because throwing an interception and turning the ball over on downs are one in the same at the point. Therefore, I'd have to imagine that the offense scores more often than usual. I don't have any actual data on it though, so I could be wrong.
What I don't think I'm wrong about is the fact that both Brady and Manning have been dominant at the end of games. Five times this season, the Patriots final drive (not counting drives with < :30 seconds remaining) started with them down by a touchdown or less. All five times, they scored a touchdown. The Giants faced this situation seven times. They scored a touchdown five times as well. Call me crazy, but I'm taking the offense.