Battery management systems (BMS) are responsible for the reliable and safe operation of lithium-ion battery packs in electric vehicles (EVs). State-of-Charge (SoC), State-of-Health (SoH) and State-of-Available-Power (SoAP) are the major battery states that must be determined by means of so-called monitoring algorithms. In this study, a comparative study of a wide range of impedance-based equivalent circuit models (ECMs) for on-board SoAP prediction is carried out. In total, seven dynamic ECMs including ohmic resistance, RC-elements, ZARC-elements connected in series with a voltage source are implemented. The investigated ECMs are verified under varying conditions (different temperatures and wide SoC range) in a model-in-the-loop (MiL) environment using real vehicle data obtained in an EV prototype and current pulse tests. In this context, LIBs at different aging states using various active materials (NMC/C, NMC/LTO, LFP/C) are investigated. Furthermore, the current dependence of the charge transfer resistance is considered by applying the Butler-Volmer equation. The dependence of voltage estimation and SoAP prediction accuracy for different prediction time horizons on SoC, temperature and applied current rate is examined comprehensively.