Those are great questions.I feel that Binas Bais Yaakov and Bnos Sara tend to have very similar girls. Smart, fun, academically strong. Bnos Sara is probably a little more inside learning. That’s not to say Binas is not, they are very focused on inside learning ,but they do have a strong hashkafa program as well. Most girls who apply to Bnos Sara also apply to BJJ. Binas has many girls who applied to BJJ as well ,but a lot of them also applied to nachlas, and a bunch to Bnos Sara. So you’re looking in the right group from what I understand of your daughter.
Machon Raaya is probably the most academic of all the schools. The girls seem like they are always working, yet they do seem happy. I think the difference is that the girls in Machon Raaya may come from homes where they have a little more leeway than a typical yeshivish family ,but they are all growing wonderful girls.
Mesoras Rochel is a great academic seminary. The diffence with this one is that the girls seem to be the class leader types and come from yeshivish families.
I think the seminaries are all trying to have a closer relationship with their students now. Most do a pretty good job. I would say each of the ones you have mentioned accomplish that quite well.
What did you mean by how does the warmth manifest itself? Hope this helped.