We have the ability to perform both ultraviolet (UV) photolysis (primarily Lyman-α photons, average E ≈ 10.2 eV per photon) and ion irradiation (protons, E = 0.8 MeV) in the same experimental setup, with ices created under identical conditions. Here we present recent results on the UV and ion processing of ice mixtures at 18 K of the composition H2O + CO2 + CH3OH (1:1:1) and H2O + CO2 + CH4 (1:1:1). H2O, CH3OH, CH4, and CO2 are all major components of ices in most astrophysical environments (whether interstellar, cometary, or planetary). Identifications and formation rates of products were measured. Results for photolyzed and irradiated ices are contrasted. We find that similar chemical products are observed in both cases and that rates of formation are equivalent for most of the major products.