Nobody denies that AOA will help your application, but seriously, step 1 scores, M3 evals/LORs, and interviewing charisma trump all of the above.
My answer will depend a little bit on where you want to do the residency. If you are looking for a match at the top programs in your specialty of choice, people from the "prestigious" schools may be considered to have an advantage that you're not eligible for if you're not with all other things equal.
I know what you're getting at here, OP, shouldn't you always choose the more prestigious school if given two choices? Nope. Consider the environment that you're in and how likely you are to get the best possible board scores. To me, if I have to pay out the wazoo in tuition and living costs, it's not going to be the school most conducive to my learning.
Also consider that places such as Harvard don't even have AOA.