Thanks for the latest round of feedback. I am flying at 2pm tomorrow and still haven't booked my ticket so I really need to so I can go pack!

I don't have time to call AA, sign up for the challenge and then figure out if my trip will be on an AA number or not. Maybe I'll do this for my return trip out in August.

I'm actually flying LHR-SFO-CLE-JFK-LHR this particular trip as I need to be in Cleveland for a week. There are no SFO - CLE direct flights with BA or AA at the date/time I need so really I only have the LHR-SFO & CLE-JFK-LHR part to credit to either scheme.

Does any of the above extra detail make a difference?

I've signed up for BAEC as its free and am about to put my flights on that unless anyone sees something above to suggest AA is a better option.

Thank you all for the help offered, I have not enjoyed making this decision and spent about 48 hours in the last 2 weeks on this forum reading about it!