They’re both top-notch programs. No program is strong in everything, so each department has its own strengths, but academic differences are negligible relative to the other differences between Duke and UNC. There is a lot of collaboration between the two universities, both in classes offered (some classes are even team-taught by Duke and UNC professors) and in excavations (they share a field school in Greece).
Yes. Penn State is also very good for related studies and the languages of the ancient Middle East (if you were interested in learning Hebrew or ancient Egyptian as well, for example).
That said, Pitt has a perfectly good classics program, and it may be a much better fit if you prefer urban colleges or dislike aspects of Penn State’s social and athletic scene. Temple is also a good option.