I think that love and obsession are not necessarily mutually exlusive. However, I had an ex who was obsessed with me for years, and believe me it was not about love and hearts and flowers, it was just BAD.
Here is a major distinction: If you love someone you will do anything for them, and I don't mean anything to win them, but anything to help them. You would not think twice about taking a bullet, giving them your last dime. etc. I guess that's just my opinion.
With obsession you're concern is not for the object's welfare, but for your own.