Well certainly before you "move away" from the USA, if you haven't already, sign up for the BA US Mastercard for at least 50,000 Avios points as you first sign up (and spend a few grand). Well worth the $95 fee. If you have other Chase airline cards like I did though, you will have to wait 2 years after you cancel that card to get the BA 50,000 points, as I found out recently.

The other difference is that there are low fare offers on occasion for those residing in the UK only (or US only), although the former seem to be much more frequent. You can sometimes, but not always, take advantage of those by simply originating your outbound flight in the country of the offer though.