In this study, we examine the coordination chemistry of benzyl dihydrazone and thiosemicarbazone Schiff bases featuring different chelation modes, steric bulk, and reactivities towards cobalt(II) thiocyanate. The tetradentate benzyl dihydrazone ligands coordinate to the Co(SCN)2 fragment to form CoN6 coordination spheres (1–3), whereas the thiosemicarbazone ligands provide CoIII complexes featuring CoN4S2 coordination spheres (4 and 5) and charge-balancing anions {SCN– and [Co(SCN)4]2– for 4 and 5, respectively}. Hirshfeld surface (HS) analysis revealed a substituent effect that results in an increasing number of H···H contacts in the order –H < –CH3 < –Ph (1–3, respectively). The H bonding in 4 and 5 as well as the associated energies were computed by the DFT approach, and these interactions appear to be crucial for the formation of the supramolecular systems. The DFT study also suggested that the H-bonded dimers in 5 are examples of the recently described “antielectrostatic” H bonds.