Many LACS believe part of their mission is to ensure that their students have enough of a background in different topics to think broadly across disciplines, so once you get past “totally open”, a big differentiator is how they do that. For a truly undecided kid, an arrangement that requires them to do some serious sampling in really different areas can be a blessing whereas to another, it’s a curse.
Take a look at the course catalog and what’s required in general as well as for the considered majors. For many, you end up at pretty much the same place even with different policies.