Originally Posted by
TheEngineer
I fly TATL up to 3 times a year in Y (

) tends to be purely price based but not against spending a little more for a flight on a carrier if there are FF miles (which I suppose is the whole point of them!).
There's miles and then there's status.
On both counts, it'll be a lot easier with AA if you are price-based economy.
BA wil only give you 25% miles flown in deep discount economy, AA will give you 100%.
BA you'll probably never get to any elite status with their "tier points" system with that few flights, while AA you'll likely get Gold no problem* (which will give you a 25% bonus on AA flights, thought not on BA intra-Europe flights) and will give you preferred seating (including being able to reserve exit row seats on all AA metal flights).
*Well, it depends
how far into the US you're going to fly TATL. If you fly 3x LHR-LAX a year, that's over 32000 miles, and you only need 25000 flight miles a year to earn AA Gold status. But it's only a bit more than half of that 3x LHR-BOS, so if you're flying to the closest parts of the US only then getting to status level may be trickier.