IMO AA has better service in First. Catering is worse, though that does not mean it's bad. The hard product has advantages over BA - as mentioned it's more spacious - but it's quite dated and worn now, and isn't quite as comfortable for sitting/relaxing. Summary - I prefer the BA NF product, but if you get a good crew on AA then the service beats BA by a long-shot. I would pick AA F over BA OF personally.

The Flagship Lounge at T3 doesn't compare to Galleries. But that's irrelevant as flying OW First, you can use T3 Galleries anyway.