Flying MIA to LHR in a few months, and there are options for the above-mentioned equipment. Which is the best product in Y?

Not AA

Not nessarily so - - if you have a 773, AA in MCE is quite nice (for Y).

But if you aren't in MCE 10 across is tight and miserable. But the OP is probably talking about the 772 and BA is going to be better than that.

Do you have OW status?

If so you may get MCE on AA

If not, there is not a great deal of difference IMHO. Certainly the a380 will be newer with better IFE

for the average, non-status passenger with no inclination to pay extra for premium seats or seat selection fees the BA A380 is best.
Very comfortable and quiet new plane, good IFE. 10-across seating is way nicer than in a 777 here.

The AA 777 will likely be a 777-300 - nice new plane with state-of-the-art inflight entertainment system and power, BUT sardine-like 3-4-3 seating in narrow and cramped seats.

BA 747 - old, loud and rattly. Here as well, terribly dated IFE and no power.
I avoid those if not seated in the upper deck or in row 1. BA is in the process of refurbishing those, but that's a long way from being completed.
Also, the 747 flight is the early departure, which is less than ideal as most people will struggle to fall asleep after meal service with their body clocks still set on Florida time.
The A380 flight and the two AA 777 flights are timed better with their evening departures.

One more aspect: If you don't finish your trip in LHR but connect to elsewhere on BA, it's preferable to fly BA instead of AA as AA lands in T3 and the BA connecting flight likely leaves from T5 - the terminal transfer from AA in T3 to BA in T5 is a pain, involving bus rides and long walks.

On BA, advance seat selection only free at check-in, so make sure to check in online right when that opens 24 hours before departure. Try and snag a seat on the upper deck for the best experience.

MIA uses T3 even for BA, so no matter what if the OP is connecting onward he is going to have to do the T3-T5 shuffle.

Thank you all for your input! By that time, I will be Qatar Plat/OW Emerald. Would this get me premium economy in either AA or BA? Also, what are the best lounges I can use in MIA and LHR with my status?

If you buy an economy ticket, expect to go economy. You will not in general be upgraded just because you have OWE status. Infact I wouldnt be surprised if BA is less likely to upgrade you as a OWE, because there are anecdotal reports that if an OpUp is necessary, they often pick regular Y flyers to give them a taste of a premium cabin so perhaps they will pay for a premium cabin ticket next time. If you are a OWE, you presumably know all about premium cabins already. If you want to go premium economy, then buy a premium economy ticket.

I can't comment on what AA do for non-AA OWEs as I use the AA program.

If you are OWE, you can use any OW first class lounge. In T5 LHR (if you take BA) then that is Galleries First (next to the Concorde Room, not the other Galleries lounge at the opposite end of the terminal) or in T3 LHR you can use BA Galleries First or the AA Flagship lounge, or the CX lounge if the refurb is finished by then.

OWE will get you free access to MCE on AA. It will also get you access to free advanced seat selection in economy on BA (you usually have to pay for advanced seat selection on BA).

Premium economy is a separate class and it will not get you that.

Also, at least one of BA's 747 has bedbugs, so the other two options may be preferable.

My first post so be gentle with me!

A complete no brainer for me and it would be the A380 every time, nice and new spacious and quiet.

I don't know how other One World airlines work but on BA you I think you only get promoted up a level at the end of you membership year rather than at the time that you have earned enough points.

One of the nice things about QR is that they calculate elite qualification from a year prior to the current day. In fact, they credit miles and points so promptly that we often find they're already on our accounts when we've landed!

Based on what I've read, I'm definitely going for the A380.