Sympathy vs Empathy

Today's debate was about the difference between sympathy and empathy. The best explanation we reached was the following:

You're sad because you lost your chocolate.

Sympathy is that I'm also sad because I know how it;s like to lose chocolate and it makes me sad that you lost your chocolate.

Empathy is that i know how much you like chocolate and because you lost it, I know how sad that can be. I don't even have to be a chocolate lover to understand that.