The Shamshon Raphael Hirsch Yeshiva known as Breuer's learns in the classic Lithuanian yeshiva model, IE. Not in the Scholarly "Chochmat Yisrael" method that was taught in the Hildesheimer Seminary (Rav Dovid Z. Hoffman, and Rav Yechiel Yaakov Weinberg both Deans at the Seminary, taught in this method).
The Majority of their Rebbeim has studied in mainstream Lithuanian yeshivas such as Lakewood, Mir, and Brisk.
Furthermore, The Breuer's Shul K.A.J. history and leadership were students and family of Rav Shamshon Raphael Hirsch, and follow his legacy. As opposed to the Hildeshimer Seminary, which was started by Rav Ezriel Hildesheimer. These two great men differed in approaches. Rav Berel Wein puts it like this:
Though closely associated with Rabbi Shimshon Rafoel Hirsch, Rabbi
Hildesheimer's view of "Torah im derech eretz" differed slightly. He
saw secular studies as necessary, but unlike Rabbi Hirsch, did not
believe they were in any way spiritually uplifting. Yet at the same
time, he was much less of a separatist than Rabbi Hirsch and worked
alongside the Reform when the German government required it. Because
of this, he met with opposition on both sides of the Jewish spectrum,
yet his solutions to the challenge of modernity are echoed in the
current solutions implemented in the Jewish world today.
So, knowing the history of both institutions, there would be no expectation that the Breuers yeshiva would have a similar approach to the Hildesheimer Seminary.
From my own exsposure to students from the Breuers yeshiva, they generally move on after highschool or a couple of years in the Beis Medrash program to other mainstream yeshivas such as Long Beach, Mir Jerusalem, Lakewood, Brisk, Passaic etc.