Supported Mo-sulfide catalysts were structurally characterized by means of transmission electron microscopy (TEM), dynamic oxygen chemisorption (DOC), and EXAFS, The catalysts show the well-known MoS2 slab structures with a multilayered morphology in the case of Mo/SiO2 and Mo/ASA. The MoS2 edge dispersion was evaluated from the TEM micrographs. While sulfidation of Mo/Al2O3 results in a highly dispersed, mostly single-layered MoS2 phase, a decreased metal-support interaction (NTA addition) or use of supports with a lower metal-support interaction leads to a higher stacking degree concomitant with a loss in edge dispersion. Combined TEM and DOC results reveal that Mo/C has the highest MoS2 dispersion. Reaction rate constants corrected for MoS2 dispersion for hydrodesulfurization (HDS) and hydrogenation (HYD) of thiophene and dibenzothiophene and HYD of toluene were measured. In general, HYD rates increase with an increasing stacking degree attributed to a less hampered planar adsorption geometry of reactants on multilayered MoS2. In contrast to the HDS rate constant of the small thiophene molecule, the DBT HDS rate constant is also strongly dependent on the stacking degree. It is concluded that perpendicular adsorption via sulfur is favored for HDS of thiophene, while in the DBT case a planar adsorption geometry is preferred. Carbon is the preferred support for the HYD of thiophene and toluene, most likely due to the large fraction of corner sites. A real support effect is also found for Mo/ASA, which exhibits low intrinsic HDS activities compensated by very high HYD activity. The present results indicate that the selectivities for hydrodesulfurization and hydrogenation can be fine-tuned by the morphology of the MoS2 phase and the choice of support.