A growing interest has been devoted to turbines with diffusers, which induce a pressure drop downstream of the turbine to accelerate the fluid in the axial direction. This effect increases the axial aero- or hydrodynamic load on the turbine powertrain, such that frictional torque presents a challenge to turbine starting. Hence, this work is concentrated on how a diffuser can affect the dissipative torque of a wind or hydrokinetic turbine, in which the increased axial load and starting torque need to be considered. The approach uses a quasi-steady Blade Element Momentum model, adapted to consider the action of a diffuser, to predict instantaneous aerodynamic torque and power. The mass-moment of inertia of the entire system is taken into account, as well as the frictional losses in the bearings. As the diffuser affects the axial load on the rotor blades, the dissipative torque can undergo relevant variations. The Stribeck effect on the starting behavior of a small wind turbine is analyzed in order to evaluate the influence of the diffuser on the minimal flow velocity necessary to start rotating the turbine. The rotational speed and power output of a shrouded hydrokinetic turbine with a 10 m diameter are computed and compared to those of a bare turbine; at steady-state, a rotational speed 20% higher than that of the bare turbine is achieved, generating about 40% more net energy despite increased powertrain losses.