I currently have 6 HONDA motorcycles and have owned over 40 HONDA'S. I have ridden hundreds of different makes and models over the past 40+ years. My first ride on a "big" bike was a Harley (probably why I am a Motorcycle nut today).
Which is better? Depends on what you want! If rock solid reliability, low maintenance, electric motor smoothness and astonishing power are what you look for, then the Gold Wing. If you are concerned about anything else, I guess the Harley? Having owned a Gold Wing and working as a M/C Tech for over 20 years, the nod MUST go to the Wing! Regardless of how "good" the Harley has become, they are still high maintenance bikes. I hear all the time from my friends who ride (and love) Harley's, how much they spend on maintenance! Always "changing" this, "adjusting" that or "tightening" something!
The thing that impresses most with the Gold Wing is the power! That may not be a concern for you, but for me, performance is why I ride a motorcycle and why I do not ride a Harley! At over 100 reliable and very frisky horses, the HONDA simply cannot be matched by a stock Harley. Say what you will, a 100 horse Harley engine is damned expensive and much less reliable. There is a big difference in an engine that may deliver 100 horsepower or more on a dynomometer for a few minutes and one that will run for hundreds of hours at 100% power (as the GL1800 has done as a prototype)! Air cooling is the big minus with the H-D and a major reason that the stock H-D is down on power as well.
On the other side of the fence, the Harley does deliver better fuel mileage and has that certain "feel" that some people like or prefer. The Harley also has more leg room than the Honda, this seems to be the common complaint of all tall riders, that the Honda lacks "leg room"! Do not get me wrong, a Harley fits the needs of a lot of riders. They just do not fit my personal needs, wants or desires from a bike! Remember, there are a huge number of people that buy a Harley simply as a status symbol or another garage or trailer queen. Most of these people have NEVER ridden anything else, so they have NO point of reference on what is or is not "good" or "bad" about ANY bike! Ride both machines and HONESTLY evaluate your needs and wants along with the pluses and minuses of each machine. You may find that neither one meets your needs!
In the end, you need to decide what fits YOUR needs and YOUR personality the best. Either unit will deliver reliable performance but ONLY within the design capabilities of the machine. In the end, you are going to have to pay for and ride the bike for many thousands of miles, so you do not want to make the wrong choice. For me, neither bike does it, I PREFER my 1982 HONDA CBX! The CBX delivers the nostalgia of the Harley AND the performance of the Gold Wing in a eye catching, comfortable and still very exotic package!
Shipping back to the UK? I would bet that $2000 -$3000 USD would do it. I would GOOGLE that question!
Good Luck! Hope you enjoy your visit to the USA.
P.S. Come ride the back roads of Arkansas! Some of the finest motorcycle roads in the world!