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We investigate the distribution and evolution of H I gas in different theoretical models, including hydrodynamical simulations of IllustrisTNG and SIMBA, the semi-analytical model of GAEA, and the empirical model of NeutralUniverseMacmne (NUM). By comparing model predictions for the HI mass function (HIMF), H I-halo and H I-stellar mass relations, conditional HI mass function (CHIMF) and the halo occupation distribution (HOD) of H I-selected galaxies, we find that all models show reasonable agreement with the observed HIMF at z ∼ 0. However, the differences become much larger at higher redshifts of z = 1 and z = 2. The HIMF of NUM shows remarkable agreement with the observation at z = 1, whereas other models predict much smaller amplitudes of HIMF at the high-mass end. Comparisons of CHIMF distributions indicate that the HIMF is dominated by haloes of 10 < log(Mvir/M⊙) < 11 and 11 < log(Mvir/M⊙) < 12 at the low- and high-mass ends, respectively. From the H I HODs of central galaxies, we find that TNG100 overpredicts the number of central galaxies with high MHI i in massive haloes, and that GAEA shows a very strong depletion of HI gas in quenched centrals of massive haloes. The main cause of these differences is the AGN feedback mechanisms implemented in different models.