Remember the nose is for breathing and mouth is not. Breathe through the nose only if you can eat through your mouth!
Although the mouth is used for some breathing exercises especially while exhaling, we are not interested in physical exercises or only the elicitation of the relaxation response. We are interested in the relaxation response elicited with deep breathing seamlessly transitioning into the practice of contemplation and meditation. Mouth should stay closed and breathing should use nostrils alone.
The nostrils provide a smaller airway than the mouth does. For that reason, they are much more effective than the mouth cavity in controlling rhythm in slow and deep breathing.