Given the premise that there's no completely fair way to do overtime in a way that makes sense (the college system is dumb and is more like a shootout in hockey than it is the normal football game, and automatically requiring a 15-minute overtime puts too much stress on the players' bodies), I don't know what's wrong with the current NFL overtime rules.
The team with the ball first gets the advantage of knowing that if they score a TD, the game is over right there. But they have the disadvantage of knowing that if they don't score at all, the other team just needs a FG to win the game. And if the first team scores a field goal, the second team has a more natural "four down" advantage, knowing that they HAVE to be in four down territory until they get into field goal range - that's not something the first team really has.
So they balance out, for the most part. So why the need for a change? Just because the Patriots beat the Falcons without Ryan touching the ball in OT?