No direct experience, but I have a number of colleagues - past and present - who relocated to the US. Some chose to retain BA status, others chose to switch to a US carrier’s program.
The ones who chose to retain BA status did so because they valued the better ground experience such as lounge access for US trips, Avios redemptions for trips home, and a certain sense of nostalgia/tie back home.
Those who switched to AA did so either because they were close to an AA hub such as DFW, or because they valued the chance of upgrades on AA flights because or their anticipated US domestic travel patterns.
What aspects do you most value? How often do you plan to return to the UK? What do you expect your US domestic flying pattern to be from MIA? If 1-2 hour hops, I’d be tempted to stick with BA. If you’re looking at regular cross-country hops, a switch to AA might make more sense to increase the chance of upgrades.