I don't care for the NFL overtime, or the college version, for that matter. The coin toss is too much a factor in NFL games, and the college overtime gives us wacky scores and inflated statistics.
Analysis of NFL overtime games from 1974 to 2003 shows that 52% of the time the team receiving the kick to start overtime won, while the loser of the coin toss won only 44% of the games. However, in the 72% of the games both teams had at least one possession. So, while the winner of the coin toss wins a majority of the games, they don't necessarily do it on the first possession, suggesting other factors may be involved.
Far more important appears to be where the kickoff to start the overtime takes place. Since 1994 the kickoff in the NFL has been from the 30-yard line. In overtime games since 1994 33% of the time the team winning the coin toss has received the ball and scored on their initial possession. One would also infer from the above data, that even when they don't score on their initial possession, that they may gain a field-position advantage from the kickoff that allows them to score more easily on their second possession. Prior to 1994, when the kick-off took place from the 35-yard line, only 25% of the time did the receiving team score on their initial possession. So moving the kickoff to the 35-yard line for overtime would, statistically, eliminate the coin toss as a factor.
Another solution is the "first-to-six" proposal. This would require a team to score six points in the overtime to win; either a touchdown or two field goals. While this even further minimizes the impact of the coin toss, the incidence of overtime games ending in a tie would increase.
Don't expect a change from the current rules. The NFL likes it the way it is. Their goal, while unstated, is to get the game completed in the three hour time window. They want the 1:00 PM games done so they don't interfere with the 4:00 games; they want the 4:00 PM games done by 7:00 PM so they can show 60 Minutes, or the Simpson, or whatever their Sunday evening lineup includes.