I have a US iPhone 6S working in the UK without issue - in fact I think the US model might support more LTE bands than the UK model (not that it helps as those bands aren't used in the UK!)
You shouldn’t have an issue these days. The only issue you might come up with is with China which uses CDMA still so you’re out of luck if you have an AT&T or t-mobile phone in areas where you can’t get LTE?