Accurate prediction and minimization of axial electrode wear are critical in enhancing the machining quality and tool life in Electrical Discharge Machining (EDM), especially when ultrasonic vibration is applied. This study presents a comparative analysis of two predictive modeling approaches—Response Surface Methodology (RSM) and Gaussian Process Regression (GPR)—for modeling axial electrode wear rate (LWR) in ultrasonic-assisted EDM using copper electrodes. Experimental data were collected under varying process parameters, including vibration amplitude, pulse-on time, pulse-off time, peak current, and servo voltage. The RSM model achieved a satisfactory coefficient of determination (R2 = 0.8276), providing interpretable regression coefficients. Meanwhile, GPR with a Matern52 kernel and linear basis function significantly outperformed RSM, yielding an R2 of 0.9926. Optimization using the GPR model identified optimal machining conditions that minimized LWR. The findings demonstrate the superiority of GPR in terms of prediction accuracy and provide valuable insights for tool wear control in advanced EDM processes.