For ORD-LHR

I would take AA if taking AA90 ; AA is not as good as BA (imo) but the daytime service more than makes up for it. If taking an overnight service I would take BA

If travelling overnight

Drawback of BA is (ime) that the security checkpoint in T5 is busier than that in T3

benefits of BA are a fully flat bed, better IFE and a nicer arrivals lounge

for LHR-ORD, I would def take the BA service over AA