Studying in Europe can be a great experience as far as learning new language and cultures are concerned . Some of the University especially in the Scandinavia does the industrial research so there is get career prospect. If you do PhD in UK , the PhD only last for 3 years so you can earn your degree faster than other places. I am doing a PhD in Europe and there are number of Americans here undergoing PhD. Most of them from very reputed organization like American air force and others.

However, make sure your status and residency  in US is not affected anyway. You don't want to lose something you already have, do you?