This work performs the first systematic comparison of hydrogen- and halogen-bonded configurations of the HCN/HX mixed dimer, where X = F, Cl, Br, and I. Eleven different minima have been characterized for these four heterogeneous dimers near the CCSD(T) complete basis set (CBS) limit. For each complex, two different hydrogen-bonded minima were identified: the global minimum where HX acts as the hydrogen bond donor and a local minimum where HX acts as the hydrogen bond acceptor. A halogen-bonded local minimum was also identified for all but the fluorine mixed dimer. To the best of our knowledge, three of the minima are identified here for the first time. The hydrogen- and halogen-bonded local minima of each complex become more energetically competitive with the global minimum as the atomic radius of the halogen atom increases. CCSD(T) relative energies of the hydrogen-bonded local minima computed near the CBS limit decrease from 4.5 kcal mol-1 for HCN/HF to 2.9, 2.4, and 1.2 kcal mol-1 for X = Cl, Br, and I, respectively. Corresponding relative energies for the halogen-bonded local minima range from 4.0 kcal mol-1 for X = Cl to 2.7 kcal mol-1 for X = Br and to as little as 0.5 kcal mol-1 X = I. Harmonic vibrational frequency shifts reported here suggest that it may be feasible to differentiate between the various minima for X = Cl, Br, and I via spectroscopic analysis, as was the case for the HCN/HF dimer.