I've booked mixed BA/AA travel with both airlines, and with OTAs. All TPs have credited as expected, which is the OPs concern ... as it was mine!

I know Avios earning is sometimes less on AA, but that doesn't concern me greatly so I've never bothered to count them.

I do agree that AA's systems are generally more customer-friendly than BA's, whether involving minor rescheduling or more significant aspects such as a flight cancellation. OLCI is easier, and dynamic baggage tracking exists on the AA App. I'll leave the comparison there.