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The galaxies M82, NGC 253, NGC 1068, and NGC 4945 have been detected in γ-rays by Fermi. Previously, we developed and tested a model for cosmic-ray interactions in the starburst galaxy M82. Now, we aim to explore the differences between starburst and active galactic nucleus (AGN) environments by applying our self-consistent model to the starburst galaxy NGC 253 and the Seyfert galaxy NGC 1068. Assuming a constant cosmic-ray acceleration efficiency by supernova remnants with Milky Way parameters, we calculate the cosmic-ray proton and primary and secondary electron/positron populations, predict the radio and γ-ray spectra, and compare with published measurements. We find that our models easily fit the observed γ-ray spectrum for NGC 253 while constraining the cosmic-ray source spectral index and acceleration efficiency. However, we encountered difficultly modeling the observed radio data and constraining the speed of the galactic wind and the magnetic field strength, unless the gas mass is less than currently preferred values. Additionally, our starburst model consistently underestimates the observed γ-ray flux and overestimates the radio flux for NGC 1068; these issues would be resolved if the AGN is the primary source of γ-rays. We discuss the implications of these results and make predictions for the neutrino fluxes for both galaxies. [ABSTRACT FROM AUTHOR]