What about getting to try the AA First to ORD?
That's the large swivel seat I think. Well I'm totally happy with Club World so I only get that one on rare AA domestic substitutions, which is too different a service to compare to the Atlantic services. Personally I'd prefer BA Club World before AA 777-200 First, provided it wasn't a BA 777! But at the end of the day, these are fairly subjective things, both BA and AA First are big enough seats to accommodate them so why not try both. And let us know.
If this was an AA 777-300 (77W) I would probably be more enthusiastic about their First Suites.
One danger: AA still has 767s limping around (as has BA for that matter) and you don't want a substitution on that.