In this work, the three-setting switchable damper (SD) is selected because of its cost-effectiveness compared with semi-active (SA) and active suspension systems. The present article aims to compare the control strategies of both Fuzzy Logic Control (FLC) and Linear Quadratic Regulator (LQR) for mechatronic three-setting SD and active suspensions in terms of ride comfort considering the switching dynamics nonlinearities of the SD. A four-degree-of-freedom half-car model is utilized for this study. The switchable inerter (SI) is included in these systems to investigate its effect on the ride performance. A comparison between the active suspension and three-setting SD suspension systems with and without SI is assessed. The optimal parameters for passive suspension are evaluated. Results showed that the fuzzy control strategy gives a better ride comfort than the LQR up to 6.9% and 14% for three-setting SD and active suspension systems, respectively. The SD or active