All law schools are somewhat competitive because class ranking and grades mean a lot for jobs. Law students are also type A personalities who are accustomed to being overachievers. Also don't forget that in law school, everything hinges on one exam for each class. Schools also grade on a curve (whether they say they do or not). It's not like college.
I've found this to be true at two different law schools I've gone too, one tier 2/3 and one t14. Even if people are not "in your face" competitive, there is always an underlying sense of competition because of the system.
The least competitive schools are probably going to be schools that have non-traditional grading systems such as Yale or Berkeley. I think Stanford might have also switched to non-trad grading system.
In general, the most competitive schools are going to be those that are in cities/regions where they live in the shadow of a much higher ranked school or school(s).