The formation of the brightest cluster galaxies (BCG) is a challenge for galaxy formation theory. We performed high resolution cosmological hydrodynamical simulations with the AMR code RAMSES to study the properties of the BCG which forms at the center of a Virgo-like cluster. We compare the results of 2 galaxy formation scenarios, one in which only supernovae feedback is included, and one in which also AGN feedback is considered. Properties of the simulated BCG which are comparable with those of observed massive elliptical galaxies and BCGs cannot be obtained if AGN feedback is not considered. The stellar-to-halo mass ratio in simulations without AGN feedback appears too large when compared to observations, while it is compatible the observationally determined values when AGN feedback is included. The kinematical and structural properties of the BCG are extremely different in the two models. When we do not include AGN feedback, the BCG is quickly rotating, with high Sérsic index, a clear mass excess in the center and a very large stellar mass fraction. When AGN feedback is considered, the BCG is slowly rotating, with a significantly cored surface density profile and low stellar mass fraction.