Goddammit, I wasn't going to join in on this conversation because I wasn't really certain how to identify one face from another in terms of the topic at hand. I was browsing Imgur though and came across a couple images from a (recent, I'm assuming?) Vanity Fair spread. A few of the images stood out to me, so I felt they deserved to go here.
Bill Murray? I think it depends upon the period, but I could see him having period piece face, particularly as he's aged. The linked image for example just makes me think of some 18th century composer.
Michael Fuckin' Keaton? Both categories, I think. I think young Keaton, Modern. Aged Keaton, Period Piece.
Emilia Clarke? For my eyes and brain, her Face is dependent on how they do her makeup. By default though, if we're not factoring in makeup? Modern Face.
Amy Adams? Period Piece Face.
Now my brain's real Period Piece Face vs. Modern Face challenge?
Jon Hamm. Period Piece, Modern. My brain doesn't care. It just wants to be stuck in the wilderness with him for a few days, relying on one another to survive. There'll be an exchange of body heat. No, no, we won't be fuckin'. But we'll definitely be cuddling - for survival, you see. I'll even forego my usual placement and accept the little spoon position, if that's what he'd prefer.
ETA: The mentioned Imgur post for your lookin' needs. Some of the images are just fantastic.