We investigate the spin-state energetics and the role of ionic charges in the electronic configuration of binuclear complexes of the form [(NH3)(5)Co(py)-X-(py)Ru(NH3)(5)](q+). In these compounds with q = 4-6, py pyridine, and X = C C and C-60, the Co-Ru distance varies from similar to 1.4 to similar to 2.1 nm. We carry out a systematic electronic structure calculation using different exchange-correlation (xc) approaches within spin-density functional theory, which are largely employed to investigate the properties of a variety of coordination complexes. To evaluate the effects of spin states and type of spacer in the bridging ligand on the valence tautomerism between Co2+/3+ and Ru2+/3+, we examine in more detail the case of Creutz-Taube-type ions [(NH3)(5)Co(py)-X-(py)Ru(NH3)(5)](5+). Our analysis shows that the stabilization of low- and high-spin states critically depends on the total charge of the complex, type of X-bridged ligand, and employed xc approach to calculate the electron spin density. Importantly, the C-60-bridged group may result in a blockage of the valence tautomerism of the Creutz-Taube complex, inducing bistable charge configurations. Overall, our results also show that an adiabatic description in terms of the frontier molecular spin-orbitals for analyzing the distinct spin-charge states of these complexes may dramatically depend on the density-functional description.