Go for the FAA - it's much more practical in your situation.
Once you have it, it will be valid for life.
If you let your BFR expire you just have to do another to get recurrent - no paperwork, no retests, no fees.
You can find FAA CFIs to do your BFR all over the world. Likewise FAA AMEs.
The UK implicity validates FAA PPLs to fly over here - no paperwork, no fees.
The other way round is not nearly so practical or cheap.