Stabilization and trajectory control of a quadrotor carrying a suspended load with a fixed known mass has been extensively studied in recent years. However, the load mass is not always known beforehand or may vary during the practical transportations. This mass uncertainty brings uncertain disturbances to the quadrotor system, causing existing controllers to have worse stability and trajectory tracking performance. To improve the quadrotor stability and trajectory tracking capability in this situation, we fully investigate the impacts of the uncertain load mass on the quadrotor. By comparing the performances of three different controllers -- the proportional-derivative (PD) controller, the sliding mode controller (SMC), and the model predictive controller (MPC) -- stabilization rather than trajectory tracking error is proved to be the main influence in the load mass uncertainty. A critical motion mass exists for the quadrotor to maintain a desired transportation performance. Moreover, simulation results verify that a controller with strong robustness against disturbances is a good choice for practical applications. ; Comment: 56 pages, 12 figures, article submitted to ASME Journal of Dynamic Systems Measurement and Control, 2016 April