To elaborate on some of Veltz’s points.
Columbia is a tougher question, but NYU categorically does not accept BTLs. End of story.
There’s a new year of statistics, Northwestern dropped to 8th place (from 55.9% to 44.37% biglaw placement). Columbia is at 55.2%, Harvard 49.7%, NYU 43.2%, Yale 33.8%. But keep in mind that these are only people who went into biglaw directly from law school. It’s more prestigious to go to a judicial clerkship first, and that wouldn’t count.