Mine is a bit more of 'oneworld' experiences of late ...
I just did SFO-LHR on AA (a single flight number but equipment changes at ORD). The carrier on the ticket was designated as BA, open-dated. It's oneworld Explorer booked under D.
The reservation was made by AA and the SFO agent accepted it without any question whatsoever. I did not say anything at all, either. I upgraded with a VIPOW and the ORD agent asked if I have the cert. (SFO-ORD is a two-class service.) But I told her it was surrendered in SFO and she didn't give a **** about the ticket showing BA as the carrier, either.
I made a reservation for a BA flight and used my CX FFP number. BA seems to have picked up my meal preference (vegetarian) from my CX preference record .... I was surprised.
BA LHR lounges were very accommodating when I showed my AA emerald card. ... no hassle... but T4 First Class lounge was very crowded and Terrace was much more pleasant.
A 'none world' experience ... AA's system did not update my upgraded CX status (to saphire from ruby)! But no big deal.
I personally like this oneworld alliance much better than Star ... I really wish BA would not pull out.