Organic chemistry at Brown is a killer class. It is incredibly hard, and many incredibly smart kids get low grades and even fail. My sense is that, while Brown students are not competitive with each other and definitely not cut throat, if you are going to encounter any competition at all it will be in the pre-med community.
PLME is a whole different ballgame, of course -- but very difficult to get into.
Don't pick Brown because you think every course is an easy A and therefore you'll be a shoe-in for med school. I'll bet that goes for most Ivies -- if your goal is to get the highest grades possible for med school admissions, you might want to look at schools other than the Ivies.