I could be wrong but I believe competitiveness is less dependent on what school you go to, and more dependent upon the people in your year; or at least that is what vet students I am acquaintances with tell me. They basically said their class is very competitive; the next two classes above them are very supportive; and the people who were seniors when they were freshman were also very competitive. They said the competitiveness in their year and other years is due to the fact that the cohort just so happened to be made up of a lot of competitive, less supportive people, not because the school they went to pressured them into being more or less competitive. So I guess its really luck of the draw?
But also it seems from what they told me that competitive years are 1) less common than supportive years, and 2) not something you can tell about your cohort until you are enrolled at the school and attending classes with them. Perhaps you might want to look around/talk to the people who are being interviewed on the same day as you (not possible at Cornell because no interviews, but for other schools), and try to get a vibe from them, because they could potentially be your classmates and are the closest thing to seeing what the cohort attitude would be. Otherwise I don't think there's much you can do.