I have a penchant for writing obsessively long posts, so I’ll try to keep it brief.
Princeton emulates the liberal arts experience with promises of accessible faculty, a thriving residential community, and a nurturing atmosphere. In most of these aspects, it succeeds, but there will always be a slight barrier thanks to the high research output and demands of most faculty and the social hierarchy/elitism with the student body (eating clubs, Ivy reputation, etc.).
Williams is the quintessential liberal arts experience with a virtually exclusive focus on its undergraduates. The faculty at Williams have been selected primarily for their ability to teach and inspire undergraduates. The students there look out for each other, and the friendships formed feel more genuine and inclusive, rather than as a means to draw connections for the future.
One of my favorite teachers at Pomona was a '98 graduate of Amherst and a '06 graduate of Princeton. She gave some perspective on Princeton vs Pomona here: https://www.youtube.com/watch?v=-Hxh4Qe6DPc&feature=youtu.be&t=57m33s It’ll make more sense watching the whole thing, but it’s an hour long. Lots of great insights about the small LAC experience, and it’s quite funny too! Of course it’s just one perspective, but she’s gotten both the elite LAC experience at Amherst and the elite Ivy experience at Princeton (by serving as an assistant master for the undergrads as well).