Li/O2 battery has the highest theoretical energy density among any battery systems reported to date. However, its poor cycle life and unacceptable energy efficiency from a high charging overpotential have been major limitations. Recently, much higher energy efficiency with low overpotential was reported for a new metal/oxygen system, Na/O2 battery. This finding was unexpected since the general battery mechanism of the Na/O2 system was assumed to be analogous to that of the Li/O2 cell. Furthermore, it implies that fundamentally different kinetics are at work in the two systems. Here, we investigated the reaction mechanisms in the Na/O2 cell using first-principles calculations. In comparative study with the Li/O2 cell, we constructed the phase stability maps of the reaction products of Na/O2 and Li/O2 batteries based on the oxygen partial pressure, which explained why certain phases should be the main discharge products under different operating conditions. From surface calculations of NaO2, Na2O2, and Li2O2 during the oxygen evolution reaction, we also found that the minimum energy barrier for the NaO2 decomposition was substantially lower than that of Li2O2 decomposition on major surfaces providing a hint for low charging overpotential of Na/O2 battery.