We study the electronic properties of GaV₄S₈ (GVS) and GaTa₄Se₈ (GTS), two distant members within the large family of chalcogenides AM₄X₈, with A = {Ga, Ge}, M = {V, Nb, Ta, Mo} and X = {S, Se}. While all these compounds are Mott insulators, their ground states show many types of magnetic order, with GVS being ferromagnetic and GTS non-magnetic. Based on their band structures, calculated with density functional theory methods, we compute an effective tight-binding Hamiltonian in a localised Wannier basis set, for each of the two compounds. The localised orbitals provide a very accurate representation of the band structure, with hopping amplitudes that rapidly decrease with distance. We estimate the superexchange interactions and show that the Coulomb repulsion with Hund's coupling may account the for the different ground states observed in GVS and GTS. Our localised Wannier basis provides a starting point for realistic dynamical mean-field theory studies of strong-correlation effects in this family compounds.