I actually booked this flight as codeshare 2 days ago, although I did make the booking online, I paid for it over the phone. And yes, there was a big difference to mile earning and qpoints.
Q-points shouldn't matter unless you're on a LONE* in coach (and
who would do that???). In A/D it'll be 1.5x EQPs for either the BA or AA flight number. The issue is the elite bonus (25%/100%) redeemable miles which one no longer earns on any BA flights.