This work aims at comparing the damping performances of two passive treatments based on piezoelectric or viscoelastic patches. The motivation for such a comparison stems from the fact that the two damping treatments have been developed fairly independently, and are rarely compared. Firstly, the dynamic response of a simply supported metallic plate, equipped with constrained viscoelastic patches or piezoelectric patches connected to an electrical network, is measured experimentally. Secondly, a numerical model of the structure is set up and validated to evaluate the damping performances of both passive treatments under different configurations (for instance equal-mass and equal-thickness configurations). Finally, with regard to this work, the advantages and the limitations in using viscoelastic or piezoelectric treatments are discussed.