I would expect there to be quite a few highly competitive students at pretty much any highly ranked university. If half the class were among the top 2 or 3 students in their high school, this is pretty much just going to happen.
As one example I still remember once during my freshman year of university (at a top 10 university) I missed what the homework assignment was in my physics class, so asked a “friend” who was in the same class. His response was “I am not going to tell you because you are competition and I want to do better than you in the class”. Fortunately two other friends (without quotes this time) heard this and told me what the assignment was.
This actually might concern me a bit.
You should be careful what you wish for. As an example, I had a friend who like me graduated from MIT with a degree in mathematics. Unlike me he went on to get a law degree from Harvard, and then got a job at a prestigious law firm in New York city. He lasted literally one week. He discovered that he hated it. It was a very competitive and toxic and cutthroat atmosphere. He had the good fortunate of having graduated law school with no debt, and was able to go back to school to get a master’s degree in a different but somewhat related field and ended up on a career track that he liked and that was good for him. However, “big city competitive and stressful law firm” turned out to be the wrong the career track for him. It would have been wrong for me also.
Placement into a top law school will depend upon you and what you do far more than where you do it.
Statistics about placement of graduates from any particular university are very highly skewed by the type of student who attends each particular university. As an example, if you look at students who get accepted to Harvard or MIT out of high school, they are likely on average (not in every case) to end up doing well in life one way or another regardless of whether they actually attend Harvard or MIT. This is just because of the type of students who get accepted to these schools. Of course students who get accepted to Columbia and Duke also tend to be the type of students who are likely to do well in life regardless of whether they go to Columbia or Duke or somewhere else.
I know quite a few lawyers. They attended a wide variety of universities. They graduated university with a good GPA and did well on the LSAT. Due to the particular type of lawyers that I know, most of them got their bachelor’s degree in engineering or mathematics or computer science. However, you can attend almost any university and major in almost anything and go on to law school.
I do not think that there is a bad choice here (and this would include Dartmouth and Amherst if these are still options). I think that you should go to whichever school provides an environment where you will be comfortable and happy.