The choice of BAEC vs Aadvantage depends on your travel habits and priorities. The general rule is as follows

If you normally pay to fly on economy or discounted economy and are only after redemption tickets that do not charge fuel surcharges, then AA maybe the way to go.

If you pay to fly premium cabins and would like lounge access, fast track security, etc, then the BA scheme is better.

If you do not really fly but want to use credit card spend to collect miles/avios, then you have to see study the credit card schemes to see how earning rates.

What you have to factor in is that if you
- spend Avios
- fly on BA
any redemption ticket will incur fuel surcharges so the higher Avios earning rate may not be that good in reality.

Different schemes have different "sweet spots" so an overall comparison may not be that easy unless you have specific destinations in mind.