We performed density functional theory (DFT) calculations on binary and ternary oxo/fluoro crystals of the geochemical twin pair zirconium and hafnium to evaluate and compare their stabilities. This is the first DFT study on bulk ZrF4 or HfF4, as well as on a hypothetical ZrOF2 or HfOF2 bulk crystal. For α-MO2, β-MF4 and MOF2, we have found significantly higher cohesive energies for the respective hafnium species. This suggests a considerable gap in affinity toward fluorine and oxygen between the twin pair in the solid state. In agreement with experimental findings, this gap is slightly more pronounced for fluorine. This study is also the first to evaluate the theoretical, endothermic mono-hydroxylation of the respective fluorides or oxyfluorides to model the difference in affinity toward fluoride versus hydroxide. For these, we could also find a slight energetic preference for the hafnium compound.