I have no experience of international AA v BA, but I've flown AA domestic 'Main Cabin' and F about 4-5 times over the last 3 months and would take BA CE every-single-time. So many things went wrong with AA (from boarding to the food) and it just felt like an anxious flight. Service wasn't as good, drinks weren't topped up, the F crew member disappeared for almost an hour to help in economy and, despite what someone else said in another discussion, Main Cabin economy passengers were hanging around the front toilet a lot, so if you sat in row 1 it wasn't a great experience.

Having said that, my Austin-based business partner also reckons DL domestic F is the best option. Downside they only fly out of certain airports and for him to earn his DL points, he often flies AUS to ATL and back out ATL again simply to stick with DL!