I am an American student who chose to do an MA in the UK. I applied to schools in the US and UK so got to experience both lovely processes. My decision to go was based on five factors. 
1) The program was only a year long, letting me get my degree in half the time with the accompanied lower costs.
2) I wanted the chance to work abroad and getting the degree abroad would help make that happen. HOWEVER, the UK's visa requirements were suddenly tightened while I was there so staying was not an option and my plans had to be reevaluated.
3) I never got the chance to study abroad as an undergrad and had the thought "if I don't do it now, when will I?"
4) I've been interested in British culture for much of my life and studying there was a great opportunity to really plug in.
5) The number of Museum Studies programs in the UK seemed to be a pretty good indication of the value given to the museum industry in the UK. So many programs, so many museums, and there really seemed to be this approach to museums that they were a necessary asset to British culture, not the luxury they are often seen as in the States.

But if you're looking for a program to give you the best professional edge, my advice is to stay in the US. The strength of the education you get is based on your university, not country. But one of the biggest benefits from a good program is a sound professional network and mine is largely in the UK, although it's really a great UK network thanks to some great projects and publications I was a part of. Additionally, there isn't as much weight given to professional experience at many UK schools, with more time devoted to coursework and less to putting it into practice. The small number of people in my program who had little or no professional experience was a big surprise. 

If you're looking at getting the "education and degree alone" from your school, I don't see that there would be a huge difference. It's the network and experience that gets you the next step forward.

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