Regarding Columbia and Brown in terms of core or general education requirements, a student who likes or does not mind the Columbia core curriculum may still find Brown suitable, in that s/he would still be able to take similar courses as free electives at Brown. But not the other way around, since a student looking at Brown for the open curriculum would likely dislike the Columbia core curriculum.
In contrast, Brown’s open curriculum does not extend to ABET accredited engineering majors. ABET accreditation requires some humanities and social studies requirements, so Brown has those for engineering majors, though to a lesser extent than many other schools have.