I am looking at a 'Premium Economy' return LON-LAX-LON in May/June and am getting confused. I like to book on AA to make sure I get my AAdvantage and million miler miles etc. However, booking on AA seems expensive and never non-stop, whereas BA has direct flights cheaper. What do I lose by booking on BA? I'm guessing I'll get full AAdvantage miles if I put the right number in the right place but do I need to be aware of anything else?