A large sample of cosmological hydrodynamical zoom-in simulations with adaptive mesh refinement is analysed to study the properties of simulated brightest cluster galaxies (BCGs). Following the formation and evolution of BCGs requires modelling an entire galaxy cluster, because the BCG properties are largely influenced by the state of the gas in the cluster and by interactions and mergers with satellites. BCG evolution is also deeply influenced by the presence of gas heating sources such as Active Galactic Nuclei (AGN) that prevent catastrophic cooling of large amounts of gas. We show that AGN feedback is one of the most important mechanisms in shaping the properties of BCGs at low redshift by analysing our statistical sample of simulations with and without AGN feedback. When AGN feedback is included BCG masses, sizes, star formation rates and kinematic properties are closer to those of the observed systems. Some small discrepancies are observed only for the most massive BCGs and in the fraction of star-forming BCGs, effects that might be due to physical processes that are not included in our model.