As the mother of 2 daughters who attended Michlalah, I can offer some perspective.
One is very chareidi & one is Chardali. Both attended college & graduate school. Both are very intellectually oriented.
One took classes given by Rebbis & Morot who had a Chareidi Hashkafa.
One took classes given by more Tzioni Daati Rebbis & Morot. Both found their classes to be intellectually stimulating, with the staff open to discussion and questions of hashgafa & most importantly “how do things fit” & how do I fit in the world while holding onto my values.
Michlliala for Israeli’s is an accredited 4 year college & they take their education of both Israelis & Americans very seriously. There is no skating there, but they expect & demand that the girls fulfill their intellectual duties, this is NOT high school.
I know several girls why went to MMY. Learning is on a very high level, whith the school having a decidedly American/Zionistic hashkafa. They are very open to challenge & questions from the girls. The girls who go there are religious, but their centric approach is less “life lessons” ie; how to live your life within your religion, and more into how to fit your religion into your life.
Darchei Bina gets wonderful girls who are quite religious and want to stay that way. The learning is great, but not on a superior level. Their focus is to help the girls “firm up” their beliefs and help them figure out how to fit them into their lives. Most continue to college.
But I have to tell you that myself and most of my contemporaries (parents) would never allow/encourage our children to dorm at a secular school, the exception being Stern. Since most of my generation went to secular colleges, at all levels, we know what is involved and would NEVER permit our kids out of our influence until graduate school.
Hope this helped.