Emotional information is critical for our social life, in which attentional bias is now a focus in the study on attention. However, the attentional bias processing mechanism of emotional faces still arouses huge controversy. Using similar experimental paradigms and stimuli, the published studies have yielded contradictory results. Some studies suggest that angry faces could automatically stimulate attention, that is, there is an anger superiority effect. On the contrary, lines of growing evidence support the existence of a happiness superiority effect, suggesting that the superiority effect is shown in happy faces rather than angry faces. In the present paper, the behavioral and neuroscience studies of anger and happiness superiority effects are combined. It is found that there are three major reasons for the debate over the two types of effects, which include the choice of stimulus materials, the difference of paradigm setting, and the different stages of emotional processing. By comparatively integrating the previous published results, we highlight that the future studies should further control the experimental materials and procedures, and investigate the processing mechanism of anger and happiness superiority effects by combining cognitive neurobiology means to resolve the disputes.