I think that maybe the word I'm looking for is expressiveness. I like expressive faces - faces that can powerfully convey a range of different emotions ... and the different aspects of the person's character.
Tom Cruise is an example (to me) of a handsome but uninteresting face. I mean, there seems to be a rather limited number of expressions he can have on his face.
Completely unattractive, and yet very interesting.
Too weird to be "beautiful", but oozes quirkiness, originality, emotion.
Boy, is he ugly ... but this is maybe a good example of what I mean about a face that shows a lot about what the person's personality, mood, character etc.