My child is trying to decide between the same two schools. Also an international student, and also just turned 17. I also had the impression that Georgetown would be a warmer and supporting school, even though my daughter loved the student vibe at UCLA. But it’s really a BIG school and your daughter needs to be outgoing and self-starter to get UCLA at its best. If my child decides against a gap year (she’s considering doing that) I hope she chooses Georgetown, where I feel she would be more comfortable as a younger-than-the-rest student.
In terms of reputation, and I know that is important in Asia specially, the rankings you mention are unfair to Georgetown because they take into account factors that have nothing to do with the undergraduate experience or the quality of the teaching, such as times a published teacher/researcher is cited. Anybody who knows about colleges in the US and who would consider hiring your daughter in the future will know that Georgetown is a top school. That may not be the case of regular people in Asia.
Let us know what she decides!