Thought I would add my experience as I went thru this change.
Me and my partner have houses in the UK and Miami, USA. We moved our accounts to the US BAEC.
I have a UK BA Amex. They soon cottoned on and started sending me letters that I was violating the T's n C's for the card and had to either move my account back or close the CC.
I kind of ignorred them.
Finally the letters stopped and then got a letter saying I could keep the CC - guess they liked the business, but no miles would be posted for purchases to my BAEC account - and they don't.
I am a Brit citizen and no US SS number so can't get a US Chase card. my partner does have one tho as he is a US citizen.

My only other observation is that if u have issues, and you call the BAEC in the UK, they say "not our problem - call the BAEC in the US" which is kind of annoying - one would hope there would be a seamless "global" service offered, but it is anything but. Especially if you have used miles to upgrade etc.
Tickets are no cheaper. You get different sales, but generally they correspond to UK ones, or so I've found.
Any questions, feel free to ask.