Moto X Style (intl) and Moto X Pure Edition (US) are the same phone...WRONG!
The thread title is very misleading... They are not identical phones where it matters the most....service! After all, you are buying a phone to use as a phone right..??? Maybe not.
The Style has a few different bands for LTE service than the Pure. I would recommend buying them the Style for UK use and Pure for US use as Motorola has marketed.
Moto X Pure edition
4G LTE (B1, 2, 3, 4, 5, 7, 8, 12, 13, 17, 25, 26, 38, 41)
Moto X Style
4G LTE (B1, 2, 3, 4, 5, 7, 8, 12, 17, 20, 25, 28, 40, 41)
So, as you can see bands 13,20,28,40 are the differences. You will still get service, just not in all areas as good as if you had the appropriate phone.