There is one significant benefit to accruing miles on AA rather than BA: you can use them for AAnytime awards on AA, which are not capacity controlled. BA does not offer this option.

The main drawback is that you don't get access to BA elite phone lines, and their regular lines from the US are a nightmare (routine waits of an hour or more). Also, with BA silver or above status, you can use AA lounges when flying in the US, but you can't do that with the comparable levels of AA status (Plat and EXP).

I am accruing on AA even though I fly mostly full fare WTP (W), which would get me status on BA quickly. I do it because I get lounge access anyway on my BA flights with my AA Platinum status, and can use the miles for unrestricted awards.

(Using Avios for upgrades on BOS-LHR, while attractive on paper because of the low number of points required, is nearly impossible most of the year unless you plan many months ahead. From May to October BA releases few if any seats for Avios awards at the last minute, and the ones released early are long gone by then. I fly on BA flights with half-empty CW cabins frequently, where no upgrade awards were released. So it really is not a great benefit if you can't plan far ahead.)