Isn’t the OP trying to get to Cancun? DFW is just the stopover should they take that option?

The BA option LGW > CUN would be the older club world product, ying-yang layout (2-4-2). Where as from LHR > USA > CUN there is more chance of getting the new Club Suites in Club World, 1-2-1 layout, privacy door etc.

If we are just comparing old CW with CS, then there are lots of threads on this, many prefer CW for sleeping. CS is certainly more private for individuals, not great for couples or families.

As for AA vs BA service then I can’t really comment myself but I’d go for BA. Others will have a much more detailed answer.

For that length of flight and destination I’d rather a direct flight, connections are fine for points running but troublesome for baggage, missed connections, delays etc. Fully flat bed the whole way for me, much to the disgust of many Tier point hungry FTers!!