If you booked a biz ticket with miles then you should be put in the 'premium economy' section of the domestic (within south america) LAN flights. They block out the middle seat and make it in to a table, and give better service. I've yet to ever see anybody SITTING in that section in the half dozen times i've flown LAN within south america. Tried to see if i could get upgraded as Emerald / AA EXP and got confused answers. They told me to talk to AA about it.

AEP is the city/downtown airport. It's smaller, and much much closer to downtown. It's mostly a domestic airport so there's no entry fee for example. In general LAN is nice and if i were you i'd just take the LAN GRU-AEP leg. Call BA and try and get them to put you in premium economy.