Anyone who has studied abroad knows how one trip can alter one's life path. And, with so many schools now allowing overseas students, there's no reason why you shouldn't be able to complete your European masters degree at the same institution for another few years.
Most institutions want their students to graduate knowing that they not only learned something in class but that they have grown as people as well. This encompasses everything from learning to take care of oneself to adjusting your viewpoint as you get a better understanding of various cultures and people. Immersing yourself in different situations is the best method to do this.