It is an enviable choice, and I am sure you chose already. What did you pick?
Vanderbilt has a large advantage over Williams, for biomedical research on campus. They have a medical research facility, research hospital and an actual medical school on the campus. LACs, you go off campus typically, and you would have to go all the way to SUNY Albany Medical to find such a fine research hospital as Vanderbilt U offers.
Learning is not just about professors and classes. Learning happens student to student, and often grad student to undergrad student. Grad students are there to inspire you, warn you about pitfalls, and teach you. They are fabulous at a place like Vanderbilt!
At Williams College you will have no access to super smart PhD students and MDs, but you may have a closer relationship with a professor and your tight knit class of super smart students. Nashville is so much better socially, than small town Massachusetts, I mean it IS a city with stuff to do! . Weather is way way nicer in Nashville too, if that matters at all. More clubs, more activities, more classes to choose from. Socially, you could actually date, I don’t see how one does that at Williams, very awkward, just like high school??
Vanderbilt U is now a bit more diverse. Vandy has really pushed to bring in Asian Americans, and other groups that were underrepresented traditionally. Jewish students are better supported than ever before at Vandy.
If you live any distance, its very very hard to get to Williamstown, MA. You may need to fly to Albany and bus it. Nashville is a breeze. It offers a major airport. These may seem like small things for an intellectual student, but really the size alone is the reason to go to Vanderbilt. Do you want a school the size of your high school? Do you want to be in a boarding school crowd? Then Williams is the right pick. If you want a diverse university in a nice urban environment, pick Vanderbilt.