Correct.
If you're only flying 20k a year it would make sense to credit to BA so at least you get a couple free trips a year. Crediting your flights to AA may take 5 years to get the award you're looking for.
Then you can use CC earnings for longer awards.
Each airline generally has on their website each partner and what the earning rates are for each class.
here is the one for AA.
Click on the airline and you will see the rates.
And BA can be found
hereIts generally the discounted economy which earn lower or no credit.
So when booking a ticket look at the fare class and see what it earns.
Earning miles when flying CX is a perfect example. Only H class and higher will earn miles on AA. Whereas BA will only give 25% on fares up to H. Most cheap tickets won't book into that class.