Up until the last year and a half, I had been running a predominant running offense (roughly 75-25). The main problem I had with my run-oriented offense is that when I fell behind by 14 or more deep in playoffs, the game was basically over. At least with passing offense, there will be more drives occurring during the game, so a better chance of being able to come back from a deficit. I've opened up my offense, where I probably run about 35% of the time, and I've definitely seen an improvement in my teams.
It's not to say that you can never win the NC by running the ball, but it's just more difficult to do.