Konstantin

Exhaling and Inhaling through nose is most balancing and is regarded as more healthy due to cleaning the air, moistening and warming it, also the warm air during exhalation warms the nasal cavities. It is the main method in Qigong and Yoga-Pranayama.

Air passing and touching nervs on top of nasal cavity has an activating effect during inhalation and calming during exhalation. You can regulate in this way by choosing an appropriate combination. It is easier for beginners to regulate the speed and amount of air flowing in/out by using their mouth. Actually this can also be done by coordinating the muscles involved in breathing, by partially closing the glottis or using the soft palate.

Some examples of special cases:
Cooling inhalation through mouth in Yoga-Pranayama
Quick and strong exhalation through mouth to quickly release power