Does Princeton or Amherst have a stronger liberal arts vibe?

Amherst has the stronger classic liberal arts vibe. It is a small liberal arts college, almost all undergraduates, with a culture built around discussion-based classes, close faculty access, and broad academic exploration through its open curriculum. Princeton absolutely offers many of those qualities too, especially strong teaching and small seminars, but everyday student life still feels more like a research university than a pure liberal arts college.

Amherst will likely feel closer to what you described if you want your whole environment centered on undergraduates. The scale is smaller, professors are teaching students at every level, and there is less separation between intro classes and advanced work than at many universities. Its open curriculum is also a big part of the vibe:

Princeton fits a student who wants liberal arts teaching inside a university setting. It puts real emphasis on undergraduate education, has junior papers and a senior thesis that push deep intellectual work, and offers plenty of seminar-style learning. But it also has graduate programs, a larger institutional footprint, and more of the traditions and infrastructure of a major university, so the atmosphere is broader than the classic small-college model.

If what you mean by liberal arts vibe is discussion-heavy classes, close-knit academic life, and freedom to roam academically without much structure, Amherst is the clearer match. Princeton is a strong option for someone who likes those features but also wants the resources, energy, and identity of a major university.