If you go to Columbia you should not be going in expecting that people will not be competitive. You will certainly be shocked. Competition at Columbia is undoubtedly different from what it has been in the past, assuming the past "horror" stories are true, but it still exists and is definitely widespread. It isn't competition in the sense that people tear pages out of books in the library, but people work hard and a sizable minority guns for the top of the class.
At admitted student day, a day that is-and was for the most part-supposed to be relaxed when they roll out the red carpet for prospective students, there were several people taking hardcore notes at the panels and discussions and people definitely asked hardcore questions, like how to best make law review, how to best work for a V5, how to get a prestigious federal clerkship, etc. A lot of the prospectives I met were very nice overall, but definitely competitive, super type-A people who most likely won't all of a sudden relax upon starting school at Columbia. Conversations with multiple current students confirmed this: there is a definite competitive atmosphere at CLS in that most people work very hard with intentions (at least 1L year) of being at the top of the class. This is not to say that people aren't friendly with each other or don't go out to parties, etc, but you simply can't go to Columbia with the mentality that your peers are looking to coast through law school, because they aren't.
It's funny how a lot of people on this board try to convince themselves that competition doesn't exist at the top schools. Sure, people might not be at each others' necks all the time, but it's pretty obvious to me that law school regardless of where you go will be a BIG step-up in competition and intensity from the vast majority of undergraduate programs. I think this is especially true in the case of a native Californian who considers herself "chill" and moves to NYC to start at Columbia with the notion that it won't be competitive.
I don't think that people are tyring to make it seems like CLS and peer schools have students that coast on the school's name. Basically, it just seems that people want to be the best and will work hard--but they aren't trying to sabotage other people by tearing out pages or refusing to share outlines or what have you. Every school has its gunners and such...but as long as they don't blantantly (or covertly) try to sabotage you, then it's fine.