This paper studies the relative performance of domestic and foreign banks in the Latin American and Caribbean banking industry. Data Envelopment Analysis is used to compute technical efficiency scores for the years 2001 and 2013. Our main contribution is twofold. On the one hand, we assess performance at the level of the management of specific production factors. On the other hand, we distinguish program efficiency from managerial efficiency, which allows us to evaluate whether the differences in technical efficiency between national and foreign banks are due to the use of different technologies (program efficiency) or, conversely, differences in the managerial capacities of managers in both categories of banks (managerial efficiency). The results show that foreign banks are more efficient than domestic ones, and provide evidence that the greater efficiency of foreign banks is mostly due to the superior technology they use.