Before the Covid outbreak Amex would run occasional promos to convert their points to Avios ... it's normally a 1:1 rate the same as Aeroplan, but you would occasionally see offers of 1:1.5 or even 1:2 for even greater value.
I've done it a few times, always just waiting for one of the promos so I could get better value. Redeeming Avios against BA flights has never been a problem in either Y, PE or J ... they seem to all have reasonable availability and the hard/soft product is similar to AC ... in some cases (PE or J on the A350, for example) substantially better. Even in Y on the old 777s, BA is pretty good - especially considering you're getting TATL for what's effectively just over 20,000 Amex points (with conversion bonus) and around $375 in taxes/fees. Y product is comparable to AC but with better food. On that basis, I consider Amex points to be more valuable than Aeroplan points.
Have never tried to redeem Avios for flights on AA so I can't speak to that.