Recent advancements in automated driving technology and vehicle connectivity are associated with the development of advanced predictive control systems for improved performance, energy efficiency, safety, and comfort. This paper designs and compares different linear and nonlinear model predictive control strategies for a typical scenario of urban driving, in which the vehicle is approaching a traffic light crossing. In the linear model predictive control (MPC) case, the vehicle acceleration is optimized at every time instant on a prediction horizon to minimize the root-mean-square error of velocity tracking and RMS acceleration as a comfort metric, thus resulting in a quadratic program (QP). To tackle the vehicle-distance-related traffic light constraint, a linear time-varying MPC approach is used. The nonlinear MPC formulation is based on the first-order lag description of the vehicle velocity profile on the prediction horizon, where only two parameters are optimized: the time constant and the target velocity. To improve the computational efficiency of the nonlinear MPC formulation, multiple linear MPCs, i.e., a parallel MPC, are designed for different fixed-lag time constants, which can efficiently be solved by fast QP solvers. The performance of the three MPC approaches is compared in terms of vehicle velocity tracking error, root-mean-square acceleration, traveled distance, and computational time. The proposed control systems can readily be implemented in future automated driving systems, as well as within advanced driver assist systems such as adaptive cruise control or automated emergency braking systems.