If I'm reading things correctly, the distinguishing characteristic cannot be actions. In her Sense and Sensibility examples, characters actions seem sometimes at odds with what would be their labels.

What seems more likely is that the distinguising characteristic is the character's/person's reaction to events. The person with a heart of flesh has an internal reaction that is more likely to cause them anguish or joy. The person with the heart of stone's reaction may appear outwardly similar but will leave the person insulated from the pain or pleasure; the reaction will be muted.

I don't think that's exactly right, though, because again, from pegkerr's example, people with hearts of stone can be demonstrative. Their expressions, however, are inherently self-centered.

It's an interesting puzzle.