I'd collect the 100% AA miles on AA rather than 25% BA miles when credited to another carrier. Probably won't get any miles on BA if the fare is discount economy...

Remember AA and BA don't credit miles on each other for the transtlantic flights. For instance, you can't request AA miles for a BA flight, SFO-LHR-
SFO and vice versa, can't request BA miles for an AA flight, LHR-SFO-LHR.

But, you can certainly earn AA miles for AA flight numbers..