Of course, work permits are available for both the USA and Germany, with the USA in transition now politically and Germany not a subject I can comment on (others can?). However, you'll end up with a marketable degree whatever direction you go.
The engineering degree will ALWAYS be one that leads you to work. There is never an end to the need for engineers in the work force. There are needs for scientists, as well, but as you can tell if you read the forum, it's much more "niche specific."
Nanotechnology is an over-stated part of our future (in my opinion.) Yes, there will be jobs, but they sure aren't in large supply now. So that's the biggest risk of the three. Could pay off handsomely, but still -- large risk at this point. You could end up a chemist doing QC work in a pharmaceutical plant on the border -- and NOT doing intriguing "nanotech R&D" work.
The Biomedical engineering degree will lead you to the medical device area. A booming business, but again -- very niche specific and I'm not sure this forum addresses those niches as we are more of a life sciences forum. I'm sure that Biomedical engineering would start you off well, but you'd need a graduate degree to do your own independent work. Which brings up the subject of, "What is it you WANT to do?"
“Humility is not my forte, and whenever I dwell for any length of time on my shortcomings, they gradually begin to seem mild, harmless, rather engaging little things; not at all like the glaring defects in other people’s characters.” - Margaret Halsey