According to Ayurvedic medicine, piercing on the left side connects the mind and body and relieves the labor pain. In Chinese tradition, left side was common to get pierced by women and the right one by men.
The left side is more preferable traditionally, however, it is not a rule. When deciding the side for your nose piercing, take into account other piercings you have, the shape of your face, your hairstyle and figure out which side can flatter you more.