Compared with the traditional linear control method without a power function, a finite-time controller(FTC) can achieve better control performance due to its exponential parameter. In this paper, we comprehensively compare the performance of the FTC and linear controller(LC) both qualitatively and quantitatively, for a first-order system. We have derived a total of 11 relevant theorems that focus on the selection of control parameters for the FTC to achieve superior control performance compared to the LC. The specific content is that a series of evaluation indicators are set for both the nominal system and the disturbed system to reflect their control performance. These indicators include the maximum control amplitude, energy consumption, convergence speed, steady-state accuracy, and anti-disturbance capability. Based on the given LC, the FTC parameters corresponding to each indicator are calculated. It has been proven that there is an optimal parameter range that can enhance the control performance of the FTC while still satisfying the constraints of the evaluation indicators. In addition, it is also important to demonstrate that, under the same evaluation index constraint, there is no LC with better performance than the FTC. The significance of the research is to provide theoretical support for improving the control performance of the FTC, and to establish a theoretical basis for selecting FTC parameters.