Recently, there has been a growing interest in integrating NMPC in automotive applications in order to make driving more intelligent and ecological. One major challenge in the way of developing Nonlinear Model Predictive Controllers for automotive systems is to reach sub-millisecond computation times for real-time applications. C/GMRES and Newton/GMRES are fast optimization methods demonstrating promising results. This paper develops an Ecological Cruise Control for a Plug-in Hybrid Electric Vehicle, and then presents a comparison between the two aforementioned optimizers in terms of accuracy and speed. Simulation results tested on a high-fidelity model of Toyota Prius in Autonomie identify C/GMRES method slightly faster than Newton/GMRES method with approximately the same accuracy in the solution.