Academically these are all great and can get your where you want to go.
Hamilton is much smaller, a true LAC, with a beautiful campus in a tiny rural town. The others are in cities- Atalanta is prob a better city but Case is right in the downtown.
Both have actual campuses though. Hamilton is heavy on writing skills.
Case has a bit of a reputation for perhaps being overly academic and less fun. Emory is known for a good work/play balance and obviously better weather. But they are prob similar.
3 great choices. But I would say it’s between Case and Emory on one side, and Hamilton on the other. I would imagine most people would choose Emory over Case if it’s between those 2, and Emory is ranked higher for what that’s worth.