Precise trajectory tracking is a crucial property for \\acp{MAV} to operate in\ncluttered environment or under disturbances. In this paper we present a\ndetailed comparison between two state-of-the-art model-based control techniques\nfor \\ac{MAV} trajectory tracking. A classical \\ac{LMPC} is presented and\ncompared against a more advanced \\ac{NMPC} that considers the full system\nmodel. In a careful analysis we show the advantages and disadvantages of the\ntwo implementations in terms of speed and tracking performance. This is\nachieved by evaluating hovering performance, step response, and aggressive\ntrajectory tracking under nominal conditions and under external wind\ndisturbances.\n