To be honest, I don’t think there’s much of a meaningful difference between Brown and Chicago with respect to the things you care about. Chicago does have an amazing culture of civilized debate, in which people actually listen to one another, acknowledge valid points, and modify their positions accordingly. Not that something like that does not occur at Brown; what’s different about Chicago is that it almost never doesn’t happen, whereas unfortunately in the rest of the academic world people do tend to shout at each other sometimes. I think it’s true that both the faculty and the student body at Chicago have a somewhat higher percentage of political conservatives compared to Brown, but it’s nothing like night and day.
My children would tell you, based on the experience of their friends, that there’s an anti-intellectual streak at Brown, and that the students who choose Brown over other colleges tend to lack respect for academics. Based on the experience of their friends, maybe there’s something to that, but their friends are hardly a representative sample. (Their friends were also smart, accomplished kids you would be thrilled to have as your classmates. Just like at Chicago.) No one disliked Brown; they just didn’t care much for classroom learning. At Chicago, the classroom is pretty much the center of everyone’s experience.
As a Brown student, through your course selections, you could probably come close to replicating what the Chicago core would teach you. What you would not be able to do is make it so that everyone else you met at college shared an extensive vocabulary, background knowledge, and analytical framework for discussing ideas.How much you care about that is up to you.