AA should have access to the same QR award seats (if any) that BA has. And AA will likely cost less than BA (in both miles and cash) than BA. That said, it's possible that QR will have award seats available to its own FFP members that are not available to either AA or BA. It is possible to transfer BA Avios into a QR FFP account, if necessary. (Both BA and QR use Avios as their frequent-flyer "currency.')

But I am seeing good availability next Fall in Business Class from JFK to NBO on Ethiopian and Egypt Air via United MileagePlus: 88K miles plus minimal taxes per person, one way.