My 2 cents - as a US based traveler, stick to the US based airline unless you have status on BA.

I only fly TATL 1-2 times a year so I almost always stick to AA metal even though BA's schedule is usually at more preferred times. Even when BA has decent pricing in business, the lack of flexibility is a no-go, and the lack of realistic upgrade options is also a no-go. I, unfortunately, got stuck in Y on a LHR-LAX flight (first time in 3 years I haven't been in at least PE) but I had the bulkhead MCE row which was actually a great seat. PE had been fully sold >6 months in advance and paid J was out of my budget, in part since I have to book my LHR flights on separate PNR's from onward travel so the premium seat tax jacks up the price.