AA have LPGS and it is usually cold (unlike BA)
Bigger seat on AA.
Brusker and more mature staff on AA but that could be a plus- more of a sense of job and finish.
Food is pretty poor on both.
Amenity kit better on BA and I would say Pjs better (AA pjs are like release from prison outfit)

Unless BA is the same price (and it usually isnt) I would go AA. I got a 1st from AMS to DFW via LHR return for about £2000 recently. AA on way out and BA on way back.

If flying from LHR then T3 is better than T5 if in 1st.