An extensive parametric study of an alternative battery model, the fractional differential model (FDM), is presented for the first time over the entire lifetime of 20Ah NMC cells. The evolution of the FDM's model parameters, identified in the time-domain, is compared to electrochemical impedance spectroscopy results to assess their physico-chemical significance. This comprehensive parametric analysis shows that the FDM is able to capture relevant physico-chemical information with regards to the ohmic resistance over the entire SoC range and battery lifetime. Furthermore, the FDM's electrical performance is compared to the conventional first order RC battery model over the entire battery lifetime. Thanks to the FDM's non-integer derivatives for system states, it is able to capture intrinsic fractional derivative properties such as diffusion dynamics, charge transfer and memory hysteresis, which results in an improved simulation accuracy compared to the RC model. The comparative study showed an improved simulation accuracy of the FDM up to 85% in the lowest SoC range and a minimum improvement of 40% over the entire SoC range, considering the entire battery lifetime. Inherently proving that the FDM's ability to capture highly nonlinear battery behavior in the low SoC region persists over battery lifetime.