The two Super Bowl contestants last year were the 3rd leading rushing team and 5th leading rushing team in the NFL. In all, the 1st, 2nd, 3rd, 5th, 6th, 8th, 10th and 11th rushing teams were in the playoffs.
Meanwhile, the 1st, 2nd and 4th leading passing teams all missed the playoffs.
The reality is there is no one size fits all. Besides, establishing the run doesn't necessarily mean you have to run the ball more than you pass it, it just means establishing that you are successful at running the ball, and therefore a threat that the opponent has to worry about.