Reduction of fuel consumption, carbon footprint as well as increasing the lifetime of powertrain components of electrified vehicle, such as battery, has been recognized as a significant challenge of our century. Model predictive control strategy (MPC) is considered as a way to tackle this issue efficiently. This optimization-based control strategy selects the best control action by anticipating the system expected response. As the main contribution, this paper provides the impact of the State of Charge (SoC) estimation by the Battery Management System (BMS) on the performance of a MPC through the cost function pareto front study accounting for the equivalent fuel consumption and the battery capacity fade during the charge sustaining (CS) mode. MPC demonstrates abilities to reduce the equivalent fuel consumption and battery capacity fade respectively by 1% and 49% compared to an On Off thermostat control strategy when the battery is in charge sustaining mode. Moreover, the results show that the SoC estimation by a BMS impacts slightly the fuel efficiency and battery lifetime when MPC is the control strategy. However, the accuracy of the vehicle linear speed prediction has more influence than the precision of the SoC provided by the BMS on the MPC performance.