My two cents,

Sympathy to me is when someone recognizes our sadness or situation but can not necessarily understand the pain that you are in.

Empathy on the other hand, means to me, the person who is responding to your pain understands it and quite possibly experienced it at one time.

So the key difference to me is the level of understanding and therefore the response will be different on the coping end.

Hope I made it clear for you to understand my meanings. Cindy