Vehicle suspension systems are fundamental components designed to mitigate the adverse effects of road surface irregularities. These systems are typically categorized as passive, semi-active, or active suspensions. This study focuses on a quarter car suspension model to explore the application of two control methods, the Linear Quadratic Regulator (LQR) and the Model Predictive Control (MPC). Experimental data are collected using the Quanser active suspension experiment setup. Initially, the LQR controller is employed to optimize performance criteria related to the system state and input signals. Subsequently, the widely recognized MPC approach is used as an alternative control method. A comprehensive comparative analysis is conducted, taking into account various load conditions and parameter variations. Additionally, the study investigates system responses under varying road conditions, changes in plant characteristics, and the introduction of disturbances, to provide an exhaustive comparison of the two control methods. The results obtained with the MPC and the comparison with the findings of various authors to date allow us to emphasize that the presented results in this study significantly outperform the previous work. These outcomes have undergone rigorous validation on the physical model available in our mechatronics laboratory.