College football's overtime is better, but not much. With college's rules, the score and many personal statistics get artificially inflated.
Here's my proposal for a better system:
For the start of overtime, both teams start with their offense on their opponent's 40 (or 35 or 30) yard line, up against their opponent's defense. Yes, both teams' offense & defense are on the field at the same time. The visiting team chooses which end of the field to put it's offense on. Players may participate in play only on 'their side' of the field.
The first score wins, with the exception of a field goal (see below). A sac or tackle beyond the 50 yard line counts as a safety (and a win). An interception or fumble recovery returned past the 50 yard line counts as a touchdown (and a win). Play is as usual, but with no punts, extra points, or two-point conversions.
Remember, it's the first team to score that wins, it's not the team that scores in the fewest plays, scores using the least time on the game clock, or anything like that. All you have to do is score first (except for a field goal, I'll get to that). Generally, teams will opt to use their '2-minute' offense, although huddling is ok too. No timeouts. Only the officials can stop play for injury timeouts, penalties, and maybe the possibility of a replay review.
[For the rest of this, I'll use the Steelers and Cowboys for my examples]
If one team stops the other team's drive, one of two cases will apply:
[Case 1] If the Steelers stop the Cowboys by intercepting or recovering a fumble and returning it for a touchdown, game over, Steelers win.
[Case 2] If the Steeler's defense stops the Cowboy's on downs or with a non-scoring turnover, play continues on the other side of the field. The Steeler's offense would not need to hurry to score, they could huddle before every play and take their time. They could also win with just a field goal. They would not need a touchdown to win.
If a team kicks a field goal before the drive is completed on the other side of the field, play continues on that side of the field. So let's say overtime begins and the Cowboys drive down the field and kick a field goal before the Steelers complete their drive. Play will continue on the Steeler's side until they either get stopped by the Cowboy's defense (Cowboys win), turn the ball over (Cowboys win), or score a touchdown (Steelers win). The Steelers would not be able to kick a field goal of their own, because the Cowboy's field goal would have come first, and would therefore give them the win.
The referees would be split into two groups and they would have to cover both sides of the field. This would be good for the fans, because players could get away with a little more than usual and fans would love it!
In the event of a defensive penalty, Play would be stopped on both sides of the field to prevent a defense from helping it's offense 'buy some time' on the other side of the field.
If both teams fail to score, switch ends and repeat the whole thing until someone does.