The increasing interest in hybridization and electrification of racing cars is pushing towards the design of dedicated energy storage systems. Among them, Hybrid Battery Packs (HBPs) represent an interesting solution, especially in racing, due to the joint presence of high-power and high-energy requirements, needed to guarantee the desired race mileage while maximizing performance. To realize a HBP, a real-time control law, named Energy Management Strategy (EMS), is pivotal to properly split the power while satisfying the driver's request. In this paper, we investigate whether the control laws that emerged for traditional vehicles can be employed in the racing scenario. Considering a Formula E case study, the well-known Equivalent Consumption Minimization Strategy (ECMS) and a classical filter-based approach are compared to the race time-optimal implicit power distribution. Analyses firstly evaluate the capability of each EMS in matching the implicit solution, showing the superior performance of ECMS. Then, explicitly including each real-time EMS in the time-optimal problem, the race times are re-optimized to evaluate the actual loss of performance. Finally, we highlight how the combination of each EMS with a dedicated battery sizing strategy can influence the overall performance, closing the gap among the different power split solutions.