Just to add yet another example: earlier this year, Patriots succeeded in their one yard attempt in the 4th quarter from the 30 yard line against the Colts.
The difference is that it was a 4th and 2, unfortunately. Another is that asking a Hall of Fame-bound quarterback to gain at least two yards to win, and if not, give your defense a chance to preserve a win as the seconds are counting down, is different than going for it on a 4th and 1, in the 1st quarter, with a non-awesome quarterback.
The logic for going for it on 4th and 1, when Andy and Belichick do it, is that teams don't go for it enough.
The logic for what happened in Indy was that Brady and the defense would get five-plus attempts to run out the clock either on offense or defense, versus handing the ball to Manning at the 70 yard line, when he can easily throw the ball to a receiver, gaining yardage from a pass interference call the way the Colts do at least once or twice every time we play them (I'm not blaming the refs for falling for it; the credit is for the Colts who are good at advancing the ball to the Patriots 30 themselves whether their receivers catch it or not.) Statistically, either option was about even, and the Patriots did have the lead... so why give the ball to Manning?
While the plays seem similar, the reasons for why these plays were called, as well as their results, are completely different.
ya, know everyone forgets that the Pats THEMSELVES went for it on a 4th and 1 situation from their own 30 yard line in the third quarter of an Atlanta game. I can't remember the score, but the Pats were up by a TD at most. Since the Pats made the conversion AND the game wasn't on national TV, this decision received no criticism/second guessing.