This paper proposes a comparative study among a widely known optimal control approach (Linear Quadratic Gaussian-LQG) and a novel predictive one (Unrestricted Horizon Predictive Controller-UHPC) for the pitch control of a grid-connected wind turbine. The main challenge for the use of predictive controllers in power systems is the size of plant's model and controller's sampling time, which increase substantially the computational cost. On the other hand, the UHPC promises a lower computational cost, which is a welcome feature for power system applications. For the development of this work, first, the wind turbine is implemented at a simulation environment to allow its linearization and state-space modelling. Later, both controllers are presented and equated. Finally, the wind turbine is modelled and simulated in two benchmark systems: a Single-Machine Infinite Bus (SMIB) system and a 11-bars test system. The simulation results show that the UHPC presents lower control oscillations for external perturbations of the grid, leading to less mechanical stress on the generator, which tends to increase its lifespan.