Any particular reason for the convoluted routings with multiple stops when there are so many one stop options, across various carriers / alliances? Wouldn't it be much more comfortable to simply fly QR ATL/DOH/DXB? These days I find that the shortest flights and connections, minimizing travel time is the biggest factor for me but YMMV.

But to answer your question I would consider paying $1600 for BA F over AA J (the bedding / sleeping surface / quietness of the cabin alone would be worth it on that length of flight not to mention the significantly elevanted F&B - not a factor personally but may be to some) but probably not over QR J.