<p>This paper presents a comparative study of supervised learning and reinforcement learning approaches for the design of power management controllers in power-split hybrid electric vehicles with two degrees of freedom. While reinforcement learning is commonly used due to its ability to operate without ground truth control data, it often suffers from convergence issues, especially in high-dimensional systems. In contrast, supervised learning can leverage optimal control commands derived from dynamic programming as ground truth, enabling more stable and efficient training. We propose a supervised learning-based controller that utilizes modular network architecture aligned with practical HEV operating modes, significantly improving training efficiency and robustness across various driving cycles. Additionally, a reinforcement learning-based controller is developed without relying on cycle-dependent states, enhancing its practical applicability. Experimental validation confirms that the supervised learning-based controller offers superior performance in terms of convergence reliability, training speed, and adaptability to unseen conditions. This study highlights the practical advantages and limitations of each approach, providing valuable insights for optimizing control performance in power-split HEVs.</p>