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We conduct a comprehensive empirical study across diverse classification benchmarks (2 to 150 classes) comparing these paradigms through both quantitative evaluation and qualitative analysis of optimization traces, revealing that each paradigm excels on structurally different task types and that no single method dominates. Guided by these insights, we propose Error-Guided Optimization (ERGO), an error-driven method that iterates over the full training set in non-overlapping batches, diagnoses classification failures, and generates targeted decision rules through a diagnose-prescribe-rewrite feedback loop. 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