In this paper, the SCO2 Brayton regenerative and recompression cycles are studied and optimized for a next-generation solar power tower under a maximum cycle temperature of over 700 °C. First, a steady-state thermodynamic model is developed and validated, and the impacts of different operating parameters on three critical performance indexes, including the cycle thermal efficiency, specific work, and heat storage temperature difference, are analyzed. The results reveal that these performance indexes are influenced by the operating pressures, the SCO2 split ratio, and the effectiveness of the regenerators in complex ways. Subsequently, considering the three performance indexes as the optimization objectives, a triple-objective optimization is carried out to determine the optimal operating variables with the aim of obtaining Pareto solutions for both cycles. The optimization indicates that the regenerative cycle can achieve the maximum heat storage temperature difference and the maximum specific work of 396.4 °C and 180.6 kW·kg−1, respectively, while the recompression cycle can reach the maximum thermal efficiency of 55.95%. Moreover, the optimized maximum and minimum pressure values of both cycles are found to be around 30 MPa and 8.2 MPa, respectively. Additionally, the distributions of the optimized values of the regenerator effectiveness and the SCO2 split ratio show different influences on the performance of the cycles. Therefore, different cycles with different optimized variables should be considered to achieve specific cycle performance. When considering thermal efficiency as the most important performance index, the recompression cycle should be adopted. Meanwhile, its SCO2 split ratio and the regenerator effectiveness should be close to 0.7 and 0.95, respectively. When considering heat storage temperature difference or specific work as the most important performance index, the regenerative cycle should be adopted. Meanwhile, its regenerator effectiveness should be close to 0.75. The results from this study will be helpful for the optimization of superior SCO2 cycles for next-generation solar tower plants.