Accurate rock typing is essential for reservoir characterization because heterogeneous carbonate reservoirs exhibit complex pore systems that weaken conventional porosity- permeability relationships. This study presents a comprehensive comparative evaluation of conventional and machine learning-based rock typing techniques for the Jeribe-Euphrates carbonate reservoir in the Fauqi Oil Field, southern Iraq. Unlike previous studies that focused on a single classification approach, this work systematically compares Hydraulic Flow Units, Discrete Rock Types, the Winland (R35) method, Lorenz curve analysis, Accumulated Correlation analysis, and machine learning clustering techniques using a unified dataset. The analysis was conducted on 179 core samples with porosity and permeability measurements. Hydraulic Flow Units, Discrete Rock Types, Winland, Lorenz, and Accumulated Correlation methods were applied to classify reservoir rocks, whereas K-means and Expectation-Maximization (EM) algorithms were used to evaluate machine learning-based rock typing. The performance of each method was quantitatively assessed using regression equations, coefficients of determination (R2), variance, standard deviation, and coefficient of variation. The results indicate a weak overall porosity-permeability relationship (R2=0.2675), confirming the pronounced heterogeneity of the studied reservoir. Among all evaluated approaches, the HFU method provided the most consistent and reliable rock classification, identifying four hydraulic flow units with the lowest statistical variability (variance = 0.017423) and the most reliable reservoir-quality characterization. Although the DRT and machine learning approaches achieved high R2 values for some individual classes, their overall classifications exhibited greater variability and lower consistency. Incorporating the Winland pore throat radius (R35) improved clustering performance but did not outperform the Hydraulic Flow Units approach. Overall, the results demonstrate that the Hydraulic Flow Units method is the most suitable approach for defining hydraulic flow units in heterogeneous carbonate reservoirs, providing a reliable framework for reservoir characterization, static geological modeling, and flow unit identification.