You should post this in the 'Europe' forum. People there are more knowledgeable about the different systems.
In general, I can say that it is rather difficult to transfer medical training from one country to another. Each nation has its own system and its own demands, and usually you have to take a test and repeat some of your training, depending on the system and the stage at which you transfer. Also, most countries require a working knowledge of the language.
Right now, the EU is working on standardizing requirements for medical training across member countries, to make it easier to move around within Europe. But that won't apply to US-trained candidates.
For research it is much easier. It is quite common to move between countries for research positions; and although traditionally there have been many more research opportunities in the US than abroad, that is changing slowly. It is better now than it was five years ago, and doubtless will be better still five years from now.
