Differently than you do, perhaps- that’s probably a question you should answer here so you can get targeted replies. Everything here has been really general- everyone likes every school for SOME reason but nobody will know what you like unless you say so.
I didn’t really use the terms (very deliberately, as I didn’t know what you wanted) but the only time I used “modern” was in the capital-M sense, about Bruriah, as in a school with a Modern Orthodox hashkafa. (Which it is to an extent- it has many types of girls- but they lean more BY than other MO schools do. And I’m not sure they officially call themselves MO.)
Like, if you were to ask me, I’d say:
BYM=really yeshivish
BYR=really yeshivish
Breuer’s=yeshivish but not excessively so
Ateres=hanhala yeshivish, students not- “modern” but not Modern
MHS=weird mix- hanhala mostly yeshivish but not entirely, mixed BY and not student body
Bruriah=hanhalah mixed yeshivish and RWMO, student body RWMO
This may make perfect sense to you or you may vociferously disagree or you may think it’s gobbledegook- it’s helpful to know what your frame of reference is.