As others have said, 3.5 hour connections at LAX might not even be enough. Coming through TBIT has had us running for the plane pre covid. Our baggage had been at the carousel so long, it had been taken off by handlers and set aside. We ran for the plane in the end, took us 2.5 hours to get through 1pm immigration when all the other international planes land, and I'm assuming that's about the time you'd be coming in if connecting onwards. So hand luggage is probably not going to be your problem.

AA or BA CS, we flew both in April, I think the AA one was the only flight in Longhaul business where we got no pre departure drink, they just didn't mention it, didn't apologise, and then made up some excuse when I asked about it. We did see First class get theirs served though. Apart from that no real difference I'd say. AA has a more perchance of looking as if they'll cut you off you drink some more, but I've never hit that sort of quantity and amount (usually by then I'll have fallen asleep and not need any more). Whereas never got that feeling from BA cabin crew.