Just remember that if you buy a USA bike when you bring it abck to the UK you will have to pay VAT. But apart from that there's no problem. I did this last eyar. Bought a bike in Alaska and rode down to Panama. No issues at borders or anything like that. It costs less as you don't have to fly a bike to America, but costs more if you bring it back to the UK (VAT) so evens out. Bikes are probably cheaper to get in the US but you are either buying before you see it or spending a few days getting a bike when you get there.
Neither option is better. I'd say if you can find a bike in the US that you like, and is a good price, go for that.