The OP doesn't really give enough info to give any form of definitive answer. What class are you flying, is it a discounted fare, what is most important (miles, service, seat, price etc)?

However, some thoughts:

Yes - you will get AA miles if you fly TATL ex Canada even if starting in US.

Warning - if you fly BA on discount economy ticket you will only get a reduced percentage miles - not worth the extra hassle of flying via Canada IMO.

If flying economy, I don't think AA is really any worse than BA (except you have to pay for your drinks)

If you have AA status, then try to snag a row 31 window / aisle seat - bags of leg room and reasonable comfort - much better than any standard BA seat.

If AA miles are really important, look for flights from LGA-LHR or EWR-LHR on aa.com. This will give you routings via ORD at little or no extra cost.