If you are buying discounted coach tickets and earning miles for free flights has any value to you, you should stay with AA for the time being. BA, IMO, has a slightly better Y product than AA (e.g., widebodies on your route and free drinks) as well as vastly better J product (which may not be relevant for you) but you will only earn a very reduced percentage of miles if you travel on a discounted coach fare. As noted above, fees on claiming an award on BA are substantially higher than on AA. BA offers a great deal on an upgrade award to J from premium economy (no copay and only 25K miles roundtrip), but that will be off a fare that is generally (though not always) higher than the lowest you can find on AA, and it will take you longer to earn those miles flying on BA than flying on AA if you're in the back in a cheap seat. (CC earning, however, is a different story.) I can't speak to UG availability BOS-LHR, but BA has been limiting it ex-JFK once again this year, so this may be a laregely illusory deal.
No one knows how these programs will shake out after ATI is implemented, so watch and wait for the future.