This study performs a comparative analysis of three Model Reference Adaptive Control (MRAC) schemes grounded in Lyapunov theory. Specifically, it compares a pure MRAC controller with two hybrid MRAC-PID schemes, each integrating the PID component in a distinct manner within the control structure. The aim is to address a significant gap in the existing literature related to the lack of comparisons involving the different ways the MRAC and PID control can be hybridized. The developed controllers undergo extensive testing in simulated scenarios emphasizing model reference convergence and disturbance rejection. The results underscore that hybridizing the MRAC mechanism with a PID controller offers notable advantages in both performance and robustness, especially concerning disturbance rejection, a scenario in which the hybrid controllers improved by around 70 and 75% the mean square error obtained with a pure MRAC controller. In general, these findings highlight the potential benefits of combining MRAC and PID techniques, providing insight into the improved control system performance that PID control can bring to conventional MRAC schemes.