I looked at the LTE support page at
https://www.apple.com/iphone/LTE/ and it doesn't look like the UK iPhone 6 supports the big two LTE networks in the US which are from AT&T and Verizon. You will have service from Sprint but my personal experience of their service is terrible.
If you plan on staying in the US for a few years for work then I suggest getting a Verizon iPhone because they have the most LTE coverage in the U.S. Depending on your data usage you should expect to pay around $70-$100/month on Verizon for 3-6GB/month with unlimited text/voice. AT&T has similar a pricing structure.
If you will be here briefly or don't want to deal with the hassle of buying a new iPhone from over here in the U.S. then bring your phone and see how the Sprint service performs.