Ultimately, it depends on where you want to work. For any business school, the network is the stronger the closer it is to the school. For Oxbridge, obviously the network will be the strongest in UK/Europe. I'm not sure how difficult it is to get visa sponsorship in the UK, but it's definitely possible, although I'm sure your employer selection will be limited (some employers don't sponsor). As far as working back in the US, I would imagine you will have to do a lot of networking. How easy it would be will depend on how strong the alumni network is in the US in your target industry. I don't think Judge has a strong network since it's a relatively new school (Said would be even worse). Also, the leadership development programs will be very difficult to break into, since those focus heavily on on-campus recruiting.
Although an one year MBA may sound attractive, I would look twice before joining, especially if you want to switch industries. With a two year program, you'll have the opportunity to test the waters by doing an internship. The internship will also give the employer an opportunity to evaluate you. From an employer's perspective, it is a risky and expensive to take on someone with no experience. However, it's not impossible to switch either. You just need to do more leg work. One good thing about going to Oxbridge is that the competition for jobs will be lower (my speculation only). Since Oxbrdige is #2/3 school in UK (and top 10 in Europe).
The bottom line: If you want to live/work in UK/Europe, go to Oxbridge. But take career switching and job hunting into consideration.