Welfare systems are designed on geographical and membership boundaries. In terms of access to health care this implies that, as a general rule, only individuals residing in their national territory can obtain health care from providers located there. However, in the past few years medical tourism has grown at an explosive pace throughout the world and in Europe. Each year in fact a small, but significant number of European citizens seek medical treatment that is financed by their public insurer in another EU country. From an economic point of view, it is important to distinguish between the two following sources of patients' mobility: a regulated mobility, where the third payer decides to send patients abroad and patients' choice, where the patient himself decides to seek care abroad. In this article we show how the combined effect of restrictions to the use of health care, transfer prices, and mobility rules determine social welfare and its allocation between Regions. The results are quite interesting: if the price set for these patients is equal to the marginal cost of the more efficient Region, patients' mobility should be preferred to patients' choice. On the other hand, if the price is equal to the marginal cost of the less efficient Region, patient choice should be preferred. The other interesting result is a possible trade off between a static model where each Region chooses its level of cost/effectiveness and a more long-term situation, where patient mobility determines a common level for this parameter.