Lounge access on domestic itineraries (including Flagship lounges once they reopen) is the biggie I would think.
You do get MCE seating on AA as BAEC Silver (I believe even if booking BE unless they've changed that once again).
You can also earn TP in BE when crediting to BA (on AA, you get nothing that counts towards status).
just want to add in case we have a one world emerald (non aa) the increased benefits are
flagship first checkin
Free food and drink in economy
access to first class lounges in the states