When someone is sympathetic, they feel sorry that someone is in pain or hurting. Kind of like pity but not condescending in nature, more caring. When someone is compassionate, they hurt with the other person, but they try/want to do something to alleviate their suffering. There is more of a drive to help the person/group get better instead of just feeling bad for them.

Compassion = 仁慈 Sympathetic = 同情