Agree with above, pros and cons of both.

On AA's side you get the swiveling seat which can be quite nice for doing some work looking out of the window. The whole mechanism though is a bit prone to being broken. When the bed is flat there is quite a significant gap at the side which legs and arms can drop down and I find a bit uncomfortable for sleeping. In general I find the AA crews fine but I appreciate they have a reputation of being a little bit "sassier" than other airlines. T3 lounges are good, AA flagship lounges with dining are good (excellent food in MIA IMHO). The amenity kit is rubbish. Pyjamas are nice.

On the BA side there are quite a number of different configs available- 777, refurb'd 777, A380, 787 new suite etc. I like them overall and agree that the privacy is a bit better than AA. 1A on the A380 is very private indeed. The middle seats are very nice with a companion. Amenity kit slightly better than AA. Pyjamas are OK but I miss the BA First branding...!!