As a psychologist, I would say that what determines whether I would treat something as an obsession or a passion is that an obsession can interfere with daily functioning. A passion enhances your life and is generally seen as a positive aspect of your life. An obsession takes over and rules your life.
A specific example that I have encountered would be religious practice. I have seen clients who experience an overwhelming passion for their religious views and life. Religion enhances their own lives and helps them face adversity. On the other hand, I have come across individulals with OCD who would not let themselves enter any doorway without reciting 10 'Our Father' prayers or would not leave the house without performing various rituals such as making a specific number of signs of the cross.
If you can look at something I say 'this enhances my life' it's a passion. If it is ruling your life, causing you distress and limiting your daily functioning I would suggest that it might be an obsession.