Going with BA is far better - flying international on American is a horrible experience...and if you're trying to move to business class, BA is far superior. FYI, connecting at LHR terminal 4 is not bad - but going between LHR terminals is a total nightmare.

MIA-LHR arrives at Terminal 3, and LHR-ZRH departs from Terminal 4.

Going between terminals at LHR can be a nightmare. Probably the worst transfer experience I've ever had. Sounds like the OP has decided what to do for this trip, but for future reference I suggest avoiding LHR whenever possible.

Not sure I understood the post about getting good seats on BA 24 hours in advance. Unless the plane is not very full, someone gets stuck with bad seats, so why wouldn't it be the OP?

BA is stingy with advance seat assignments. I think only BA Gold frequent flyers (equal to Oneworld Emerald = AA ExecPlat) can reserve seats in advance. BA does offer the option of checking in online 24 hours prior to departure, at which time you can choose pretty much whatever seats you like. If you check in at T-minus 23:59, you usually have almost the whole plane to choose from.