In the evaluation of the vibration mitigation effect of a nonlinear energy sink (NES), the selection of performance measures is important. Based on a square root model, this paper aims to propose new reasonable performance measures and new design criteria of the NES in harmonic excitation. To broaden the application range of the slow invariant manifold, coordinate correction is carried out for the square root model of the bistable NES. Two original performance measures (the displacement amplitude of the main system and the energy dissipation rate of the NES) and two new performance measures (the mechanical energy and the input energy of the main system) are compared. The optimal geometric configuration and response form of the NES are found in different excitation conditions. The results show that the energy dissipation rate of the NES is not competent to evaluate the performance of the NES in harmonic excitation, while the two new performance measures show competence. By adjusting the geometry parameter, the nonlinear vibration absorber with positive linear stiffness and the bistable NES show optimal vibration mitigation effect in small and large excitation amplitudes, respectively. The optimal response form is the periodic response rather than the strongly modulated response.