If you want to use an AA award, you must use AA miles under the terms and conditions of the AA program.
If you want to make a BA award, you must use BA avios under the terms and conditions of the BA program.
You can redeem on any oneworld airline (eg Cathay) for either type of award.
I appreciate the help. In order to book on Cathay for example and use AA or BA points, do I have to enroll with Cathay as well? Can points from BA and AA be used for the same booking?