It's probably not the BA part that will be the issue.
Assuming you are Club Europe on BA they seem to allow a garment bag as well as a roll on and a personal item even though this is not policy.
With a very chunky suit bag you would be pushing it but I would probably expect to get away with it and the worst case would be to be asked to gate check my roller.
Whether AA in J are as lenient I don't know.
If you are forced to check your roller as well as your other checked luggage it will be free on BA (2 bags in J). But I don't know if that would cost you on AA. My understanding was that US carriers were less lenient on this as that is how they make a large chunk of their revenue.