Dear elcrusoe,
I can't believe that someone needs to ask such question. Once upon a time I had conversation with guy who worked at European Commision and he was in charge of job rights within EU. And he told me that no one had created EU and free labour market for ATC and for ATCOs. It is very sensitive area( security) but what is the most important is question of local unemployment rate. Why Spanish goverment will give job me at Cannaries or French goverment will give job at Cote Azur. The best places are reserved for the best nation sons and daughethers. As someone who doesn't believe that shortage of controllers exists please explain me why we will hire bloody foreigners. Believe or not but ATCO job is still premium job in many countries. Also there is language issue and you must know language of this country ( because no one in Europe speaks European language) and it could be problem. They always could say that your language skills are not at satisfied level even in many cases you don't need local language to work. The only bright example is Mastricht but requirements are so high that 90% of currently employed ATCOs wouldn't be able to pass first phase of OJT.
If you have more such questions I will be ready to give answers.