My main question is basically, do any of you believe that there is an inherent tradeoff between going to a school with a "cutthroat" student body and a school with low national prestige and ranking?
I think you're making an enormous generalization here. Any law school you attend, regardless of ranking, prestige, etc. is going to be competitive and perhaps, yes, cutthroat. The main reason? Take a look at some of the want ads for attorneys. Most look for an individaul graduating in the top 10-20% of their class with sometimes substantial extra-curricular activities, regardless of the school that they graduate from. Moot court is competitive. Getting onto law review is competitive. Most students compete to 'book' (award) classes. And for a number of schools, grades are determined by performance. Only a certain percentage of students will receive A's regardless of how well all of the students do. It's not like undergrad where 90-100 is an A, 80-90 is a B, etc. You are working basically against other students for your grade.
At least that has been the experience of the husband that I just put through law school...