If you’re not sure you’d like the core curriculum then don’t bother applying to Columbia. From what I’ve heard it really defines the first 2 years of your Columbia experience. It makes up the majority of your freshman and sophomore classes and plays a part in conversation with your fellow classmates and creates an ‘intellectual community’ if you will as you are all taking the same classes at similar times. It is very humanities orientated and some people absolutely love it but it isn’t for everyone and if it isn’t for you then Columbia isn’t for you.
I’m going to disagree with other posters and say that Columbia and Brown ARE similar because they attract the same type of student: intellectual (note that is not the same as smart). Both the core curriculum (which is almost all made up of small, discussion based, humanities class and the open curriculum and the option to take classes pass/fail appeal to students who are very intellectual curious and want to delve more into areas of interest to them and areas which they think may be of interest to them. Although they are different approaches to education they foster the same ideas about academics. But I guess it depends on why the open/core curriculums are attractive to you. If you love the open curriculum for the freedom or the core for its structure then both would not match your interests but if you love them for the intellectualism they foster then both may very well appeal to you.