R’ Schachter is not a real fan of either. His main critique of the MB is #6 that PAA just said. And his main critique of the AH is that his Mehalach through the Sugyos is very often Mechudash and against Rishonim.
R’ Schachter is also famous for saying that when there is a Machlokes between the MB and the AH, you should Pasken by whoever is right. And if you’re not yet Higia L’hora’ah (which according to R’ Schachter means you know all of Shas and are holding in the Rishonim and Achronim in this particular Sugya) then who gave you the right to choose between the two anyway.