CC & NY are both worldly outside of the realm of Torah. NY is more integrated into the Yeshivish velt while CC is its own ‘sphere’. CC is strongly into Harbotzes Hatorah and elitist in that sense.
There are subcategories in CC depending with which Rebbe the bochur is connected. They are a Mussar Yeshiva and are sincere & real about working on Middos. They do not usually belong to the Machmir Club and can’t fathom the learning of Briskers.