This paper presents a comparison of linear and nonlinear Model Predictive Control (MPC) strategies for trajectory tracking Micro Aerial Vehicles (MAVs). In this comparative study, we paid particular attention to establish quantitatively fair metrics and testing conditions for both strategies. In particular, we chose the most suitable numerical algorithms to bridge the gap between linear and nonlinear MPC, leveraged the very same underlying solver and estimation algorithm with identical parameters, and allow both strategies to operate with a similar computational budget. In order to obtain a well-tuned performance from the controllers, we employed the parameter identification results determined in a previous study for the same robotic platform and added a reliable disturbance observer to compensate for model uncertainties. We carried out a thorough experimental campaign involving multiple representative trajectories. Our approach included three different stages for tuning the algorithmic parameters, evaluating the predictive control feasibility, and validating the performances of both MPC-based strategies. As a result, we were able to propose a decisional recipe for selecting a linear or nonlinear MPC scheme that considers the predictive control feasibility for a peculiar trajectory, characterized by specific speed and acceleration requirements, as a function of the available on-board resources.