In through your nose and out through your mouth.
Provided the air gets to your lungs, it really doesn't matter. "In through the nose" warms up the air and filters out "stuff", so, on balance, that is probably better. Elite athletes (apart from sprinters) tend to do most of their breathing through their mouths.
Threw your nose out your mouth.
Googling the first sentence of the two sentences in your question gives the following results from two different internet sources:
In general: Nasal breathing is healthier than mouth breathing for several reasons. Your lungs take oxygen from the air, and absorption of oxygen happens mostly on exhalation. Exhaling through the nose, which is smaller than the mouth, creates greater air pressure and therefore a slower exhalation.
There is some thought that mouth-breathers may not be getting all the oxygen they need, which can lead to fatigue and,in some situations may cause stress to the heart and lungs. In terms of dental health, breathing through the mouth can dry the oral cavity and lead to bad breath, gum disease and tooth decay.