The Beit Midrash or the Shul Which is Holier And Why?

So there's an idea that the BM is holier. Why? Is it simply because Torah study is great or something of that nature? No, it's because Judaism is a religion of complete life. We don't just act one way in the house of prayer and another in the world. By studying Torah, we learn what to do when we are out in the world:

Says Rav Hirsch: "Now, it is just because our Houses of G-d and the Divine services within them are not the essence of our worship of G-d, but are rather places and occasions for preparing ourselves for the worship of G-d in practical life. They take but second place in holiness compared to the Batei Midrash, houses of learning, which are devoted to the studying and teaching of the Torah. i.e., the inquiries into the prescriptions of the Divine Will as to how a G-dly life should be led by man."

R' SR Hirsch
Collected Writings Vol. I p.192
Cited in Rabbi_Beinish__Ginsburg/Behar-_Serve_Hashem_Everywhere

So you'll hear people spin this around and make the cultic seem like the ideal, that Torah study is just for study sake and that's why the BM is better. This is the opposite of how R' Hirsch approaches it. The very reason the BM is holier is because it applies to life.