This work presents a comparative examination of an Adaptive Proportional-Derivative (Adaptive-PD) controller together with a Linear Parameter Varying - Model Predictive Control (LPV-MPC) method for Quadcopter trajectory tracking. The Adaptive-PD controller modifies its gains in response to position and velocity errors to enhance resilience to fluctuating flying conditions and provide robust control for the Quadcopter. At the same time, the MPC framework utilizes the LPV model to optimize control inputs within mixed state and input constraints. We examine the efficiency of this method in a simulated environment utilizing Python, with the quadcopter assigned to adhere to different trajectories. The system integrates realistic dynamics, encompassing drag forces affecting the Quadcopter. The simulation findings indicate that the Adaptive-PD method attains enhanced tracking precision with reduced error margins in both position and orientation, owing to its adaptive optimization features. The Adaptive-PD controller provides computational efficiency and high performance for both simple and complex trajectories. The research underscores the compromises between computing complexity and tracking accuracy, offering insights into the suitability of various control strategies for quadcopter navigation in dynamic settings.