When you are sympathetic towards someone, this means that you are showing concern towards another person who is obviously in pain or is currently suffering from something. When you are empathetic, this means that you are trying to put yourself in the position of the person who is suffering from whatever the person is going through.
When you are empathic, this means that you have a high degree of the emotions that the person is feeling. When you are empathic, this is actually the same as empathetic, but empathic is considered to be the older word that is used. It will be easy for people to show sympathy, but not everyone can be an empath.