We study the effects of local environment and stellar mass on galaxy properties using a mass complete sample of quiescent and star-forming systems in the COSMOS field at z . 3. We show that at z . 1, the median star-formation rate (SFR) and specific SFR (sSFR) of all galaxies depend on environment, but they become independent of environment at z & 1. However, we find that only for star-forming galaxies, the median SFR and sSFR are similar in different environments, regardless of redshift and stellar mass. We find that the quiescent fraction depends on environment at z . 1, and on stellar mass out to z ∼ 3. We show that at z . 1, galaxies become quiescent faster in denser environments and that the overall environmental quenching efficiency increases with cosmic time. Environmental and mass quenching processes depend on each other. At z . 1, denser environments more efficiently quench galaxies with higher masses (log(M/M⊙)& 10.7), possibly due to a higher merger rate of massive galaxies in denser environments, and that mass quenching is more efficient in denser regions. We show that the overall mass quenching efficiency (ǫmass) for more massive galaxies (log(M/M⊙)& 10.2) rises with cosmic time until z ∼ 1 and flattens out since then. However, for less massive galaxies, the rise in ǫmass continues to the present time. Our results suggest that environmental quenching is only relevant at z . 1, likely a fast process, whereas mass quenching is the dominant mechanism at z & 1, with a possible stellar feedback physics.