We study the radiative decay of the 2s state of one-electron and one-muon ions, where the two-photon mechanism plays an important role. Due to the nuclear size corrections, the radiative decay of the 2s state in the electron and muon ions is qualitatively different. Based on the accurate relativistic calculation, we introduce a two-parameter approximation, which makes it possible to describe the two-photon angular-differential transition probability for the polarized emitted photons with high accuracy. The emission of photons with linear and circular polarizations is studied separately. We also investigate the transition probabilities for the polarized initial and final states. The investigation is performed for ions with atomic numbers 1≤Z≤120.