I think the nose... I'm totally making this up from what I know but I think that because through the mouth it goes directly to your stomach and through the nose it is designed to catch the bad stuff so it will filter more of the bad stuff then the mouth.
Some of these answers are interesting.... It makes no difference because both allow the smoke to get to your lungs. FYI, the small hairs inside the nasal passages are useful for filtering out dust, pollen, and other stuff in the air we breathe. It's not going to filter out the carcinogenic chemicals present in cigarette smoke. Also, breathing in anything through your mouth doesn't allow the substance access to your stomach or any part of your digestive tract. There's a little flap at the back your your throat that opens and closes based on if you're breathing or swallowing something. Sometimes, it gets a little messed up, which is why we say we swallowed wrong and cough whatever it was out of the trachea. But most of the time it works just fine.