The organic chemistry occurring in interstellar environments may lead to the production of complex molecules that are relevant to the emergence of life. Therefore, in order to understand the origins of life itself, it is necessary to probe the chemistry of carbon-bearing molecules under conditions that simulate interstellar space. Several of these regions, such as dense molecular cores, are exposed to ionizing radiation in the form of galactic cosmic rays, which may act as an important driver of molecular destruction and synthesis. In this paper, we report the results of a comparative and systematic study of the irradiation of CH₄:H₂O ice mixtures by 1 MeV protons and 2 keV electrons at 20 K. We demonstrate that our irradiations result in the formation of a number of new products, including both simple and complex daughter molecules such as C₂H₆, C₃H₈, C₂H₂, CH₃OH, CO, CO₂, and probably also H₂CO. A comparison of the different irradiation regimes has also revealed that proton irradiation resulted in a greater abundance of radiolytic daughter molecules compared to electron irradiation, despite a lower radiation dose having been administered. These results are important in the context of the radiation astrochemistry occurring within the molecular cores of dense interstellar clouds, as well as on outer Solar System objects.