In this work we analyze the evolution of voluntary vaccination in networked populations by entangling the spreading dynamics of an influenza-like disease with an evolutionary framework taking place at the end of each influenza season so that individuals take or do not take the vaccine upon their previous experience. Our framework thus puts in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors. Our results show that when vaccine is perfect, scale-free networks enhance the vaccination behavior with respect to random graphs with homogeneous connectivity patterns. However, when imperfection appears we find a crossover effect so that the number of infected (vaccinated) individuals increases (decreases) with respect to homogeneous networks, thus showing the competition between the aforementioned properties of scale-free graphs.