The differences between Bowdoin and Amherst are on the edges. You’ll get a great education and experience New England at either.
I’ll admit I’m biased as a parent of a Bowdoin student. Both schools have strong organized orientation programs, Amherst explores the college and Bowdoin explores Maine in small groups focused either on outdoor exploration or the common good. Maybe one options speaks to you more - Amherst is more getting done to business and Bowdoin is focused on small groups bonding while exploring the wonders of Maine.
Plus Bowdoin starts every year with a lobster and steak feast. Good luck.