I'll answer this with a "nonROSS" answer.
The "recommended" advice is to inhale through the nose an exhale through the mouth, like normal respiration.
If one breathes through the mouth while running, certain things may occur. One may experince driness of the mouth or even a certain degree of nausea. The nausea is a result of too much air traveling into the stomach (or so I've been told).
Hope this helps some,