We report on the fabrication and characterization of Ti/BaTiO₃/Pt memristive devices. BaTiO₃ films were grown on platinized silicon by pulsed laser deposition with different laser pulse energies. We prove the existence of a correlation between the fabrication conditions and the microstructure and stoichiometry of the films. It is suggested that the small grain size found on our BaTiO₃ films destabilizes the structural tetragonal distortion and inhibits the appearance of long-range ferroelectric ordering. We show that even in absence of ferroelectric resistive switching (RS), two different RS mechanisms (metallic filament formation and oxidation/reduction of the Ti top electrode) compete, and can be selected by controlling the films stoichiometry and microstructure.