Accurate estimation of internal resistance (IR) is vital for reliable health monitoring and lifecycle management of lithium-ion batteries (LiBs). This paper presents a comparative analysis of two advanced learning frameworks—Long Short-Term Memory (LSTM) networks and Physics-Informed Neural Networks (PINNs)—for IR estimation using real-world cycling data. The LSTM model captures short-term temporal dependencies in battery behavior, whereas the PINN model integrates electrochemical knowledge into the training process to ensure physical consistency. Experimental evaluations show that the PINN model outperforms LSTM, achieving a Root Mean Squared Error (RMSE) of 0.0233, Root Mean Squared Percentage Error (RMSPE) of 0.082, and Mean Absolute Percentage Error (MAPE) of 4.462. In contrast, the LSTM model shows slightly higher prediction errors, particularly under long-term operating conditions. These results underscore the advantage of embedding physics-based constraints to enhance model robustness and generalization, positioning PINN as a more reliable approach for real-world battery diagnostics and predictive maintenance applications.