In hybrid perovskite materials, the organic cations are one of the key structural components used to tune the electronic and optical properties of this promising class of materials. Here, we studied the strong impact of organic cations, methylammonium (MA) and formamidinium (FA), on halogen vacancy and interstitial migration, as well as surface degradation in cubic-phase MAPbBr3 and FAPbBr3 crystals using density functional theory calculations. We found Br vacancies and interstitials have much lower formation energies and higher density in MAPbBr3 in comparison to FAPbBr3 crystals. Moreover, the transition energy barrier for Br migration through vacancies within the bulk phase is lower in MAPbBr3 than in FAPbBr3. We also found that FAPbBr3 has a much higher rotation barrier of the organic cation than MAPbBr3, which points to a much stronger H-bonding with Br in the former case. Our results show that incorporating organic cations with the appropriate structure, shape, and strong H-bonding capabilities in hybrid perovskite crystals is very beneficial for suppressing ion migration and thus further improving the performance of hybrid perovskite-based devices.