Appreciate the advice. While I'm Exec Plat with AA, I know about the restriction against acquiring miles on BA transatlantic.
I'd much prefer the BA non-stops from SFO -- LHR: that's part of the reason for the question. I think I'll just accumulate the miles in a new program, rather than AAdvantage.
So: since I use a lot of transpacific flights, any sense for whether BA or CX is better in terms of a) accumulating miles for tier status; b) better perks once you get tier status; and c) better FFP service (which goes to your point about BA Exec....)