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Compassion is a general sense of largesse, and empathy is a specific type of largesse, born of feeling the pain of another as if it were your own. When using the word to describe a feeling rather than an action, empathy is a wholly contained subset of compassion. If you are empathetic, you are also compassionate. But the converse is not always true.

Also I think one could argue that empathy is a wholly contained subset of sympathy. If you are empathetic, you are also sympathetic. But the converse is not always true.

So I've decided after writing this out, in order of increasing specificity it goes Compassion>Sympathy>Empathy. The Venn diagram would have compassion as the outside, which holds sympathy, which then holds empathy. When using the words to describe internal feelings.

But it gets a little more complex when you make them into their action form: Displaying Compassion, Sympathizing, Empathizing.

MHO fwiw