Will I get optimum 4G speeds if I use a Three UK SIM on an unlocked Verizon or AT&T Note 5 ?

[AC Question]

As you may know, the Samsung Galaxy Note 5 is not available in the UK. Therefore, I will have to buy on eBay. I have seen many listings for Note 5 64gb from Verizon or from AT&T.

I am not very familiar with the radio frequencies they use and I want to be able to use 4G with it and hopefully get the best speeds too.