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This letter theoretically compares the active reconfigurable intelligent surface (RIS)-aided system with the passive RIS-aided system. For a fair comparison, we consider that these two systems have the same overall power budget that can be used at both the base station (BS) and the RIS. For active RIS, we first derive the optimal power splitting between the BS’s transmit signal power and RIS’s output signal power. We also analyze the impact of various system parameters on the optimal power splitting ratio. Then, we theoretically and numerically compare the performance between the active RIS and the passive RIS, which demonstrates that the active RIS would be superior if the power budget is not very small and the number of RIS elements is not very large.