What I was told is that in pre-war Europe and the US, the AH was considered to be the authoritative Posek. Rav Aharon Kotler ZT”L, though, favored the MB – which is why it gained a following in the “Yeshiva Velt” after the war. As a result, the MB has now come to be viewed in the US as more authoritative than the AH.
I heard this from an old Talmid of R’ Dovid Leibowitz, who grew up in the US and saw this change happen.
an Israeli Yid