Friction stir welding (FSW) is a process that can join many materials by causing minimal internal stress without the need for a direct electric current, contrary to traditional welding methods. The effects of SiC and Al2O3 reinforcing powders on the joining of AA6061-T6 and AA7075-T6 plates, which are difficult to join with conventional welding methods by FSW, are investigated in this study. The metallurgical properties of the combined samples are examined in terms of strength characteristics to investigate the effects of the reinforcement powder. In addition, elemental analysis is carried out for the mixing behavior of the powders. Finally, we used the TOPSIS method to select the most appropriate powder types to improve welding quality. Furthermore, a game theory application is presented to determine which powder type is suitable considering the joined aluminum plate’s strength expectations.