I made a previous post about taking a trip from JFK to LHR (http://www.airliners.net/aviation-forums/aviation_polls/read.main/235497/). Most people were saying BA service would be a lot better than AA but I have to disagree.
I booked BA 744 from JFK to LHR and AA 772 from LHR to JFK. My first disappointment with BA was when they switched out the 744 for a 772. Then during meal time they made us put our seat backs up so people can eat. Half way through our flight the flight attendants made us close all the window shades on the plane because they said its going to get really bright. I found BA to be okay but a little bit on the annoying side.
Coming back AA had an 80 minute delay due to the the weather but we didn't care we just sat there watching movies. Service on AA was good and they gave us an extra meal probably because the flight back is an hour longer. I would book BA again if I can get the 747, but I would definitely flight with AA again because I thought the service was good.