We study the impact of local density and stellar mass on the morphology of ~500 quiescent (Q) and SFGs from the VIS3COS survey. We perform B/D decomposition of the SBPs and find ~41% of 10^10 Msun galaxies to be best fitted with 2 components. We complement our analysis with non-parametric measurements and qualitative visual classifications. We find that galaxy morphology depends on stellar mass and environment for our sample as a whole. We only find an impact of the environment on galaxy sizes for galaxies more massive than 10^11 Msun. We find higher n and B/T in high-density regions when compared to low-density counterparts at similar stellar masses. We also find that higher stellar mass galaxies have steeper light profiles compared to the lower ones. Using visual classifications, we find a morphology-density relation at z~0.84 for galaxies more massive than 10^10 Msun, with elliptical galaxies being dominant at high-density regions and disks more common in low-density regions. However, when splitting the sample into colour-colour selected SF and Q sub-populations, there are no statistically significant differences between low- and high-density regions. We find that Q galaxies are smaller, have higher n, and higher B/T when compared to SF counterparts. We confirm these trends with non-parametric quantities, finding Q galaxies to be smoother and having most of their light over smaller areas than SFGs. Overall, we find that the dependence of morphology on stellar mass is stronger than with local density and these relations are strongly correlated with the quenching fraction. The change in average morphology corresponds to a change in the relative fractions of blue disk-like galaxies and red elliptical galaxies with stellar mass and environment. We hypothesize that the processes responsible for the quenching of SF must also affect the galaxy morphology on similar timescales.