I've done the EZE/GIG/GRU-JFK/MIA-LHR/MAD route several times and enjoyed it immensely. AA's new J class is way ahead of BA's in every regard other than not running a tatl sleeper service, so one consideration is whether you need to be sure of a full night's sleep, in which case the GIG-LHR is long enough for that, or to ensure your last leg is on BA so you can eat in the lounge and sleep a solid 6 hours on the plane, or if you do go on AA, to pick a plane that has the 2-row J mini-cabin which is much quieter at night than the main J section where people tend to be up eating and chatting and the crew are crashing around more.