OK I will take the other position for fun. I have flown WTP many years ago and more recently AA's PE. If the BA plane you are looking at is the old WTP product, I would stick with AA no question, as the seats and IFE in particular are quite tired on the older BA planes now. If you are very confident the BA plane has their updated hard product, I would consider it personally. Not all that many changes left to fly in the queen of the skies. I have found BA's soft product to be very good (and has recently been updated), where AA's soft product on PE was more like MCE-Extra in my opinion. If the mile/qualifying situation is better with the codeshare also in your routing, I would consider that another plus.
You should have a pretty good chance of being offered the option to pay up for a J upgrade on BA also, clearly J is better on AA, but I would say less of a chance of that being offered (I am talking paid upgrades at check in assuming no status upgrades at play).
In either case if it is an overnight flight I would try and get a bulkhead seat with a true legrest for sleep, vs the little flip down footrest. I certainly don't think you would go wrong sticking with AA if you like.