As an expat (sub)urban Midwesterner, educated at H and P, who raised a kid in Coastal Elite culture, I do think that currently there is a difference between UChicago’s culture and shared aspects of HYPS culture(s). Of course, as JHS points out, intellectual kids go to all of these schools (and many others), change places in grad school, find each other, and identify as kindred spirits. But those two observations (difference/similarity) aren’t mutually exclusive.
Basically, the kids who gravitate to Chicago (a) pride themselves on working hard to understand/do difficult things and (b) aspire to be and want to be surrounded by people whose center of gravity is intellectual and whose education is well-rounded. A kid who has the choice and who does not share these attitudes is unlikely to choose Chicago over HYPS. In a world where spin/talent/connections/specialization are already highly valorized, I appreciate UChicago as a place where hard, sustained work is treated as a crucial component of mastery (and where mastery itself – vs success/recognition/“winning”-- is the ever-elusive goal).