Yes, you’d have access to Soho in JFK and Galleries First at LHR if flying in business on either. If in BA first, you would definitely have access to CCR in both directions. You MIGHT have access to CCR on the outbound if you come in on AA. On the inbound, it would be the same if on BA. But if flying home on AA, then you can’t get into T5 and you’d have access to AA first, Cathay first and Qantas in T3.

As for what to choose, it’s really a personal choice. I wouldn’t really make a choice based on hard product one way or another. And I’d just say BA soft product is probably more consistently at least decent, while AA can be variable, borderline frosty 🥶 One thing I would say is that if you’re planning to eat on the plane JFK-LHR, AA is usually pretty efficient with the service and you’ll have a bit more time to sleep. But I’d recommend skipping food anyway and eating in Soho and again in London on arrival. What about flying out in AA business and maximising sleep and then home in BA first to get spoiled?