Passive acoustic localization in complex shallow waters requires algorithms tailored to specific operational constraints. This paper investigates the adaptability, computational efficiency, and statistical performance boundaries of five matched-field processing (MFP) methods—Bartlett, Minimum Variance Distortionless Response (MVDR), Multiple Signal Classification (MUSIC), Reduced Covariance Matrix (RCM), and Rank and Trace Minimization (RTM)—using the Elba-93 sea trial dataset. Error metrics and processing complexities are systematically evaluated across stationary and maneuvering target scenarios. Rigorous non-parametric statistical tests reveal distinct operational boundaries: under stationary conditions dominated by systemic environmental mismatch, energy-based processors guarantee reliable baseline stability. Conversely, under snapshot-deficient dynamic conditions tracking a receding target, standard high-resolution subspace methods become highly vulnerable to trajectory jumps. In such highly dynamic scenarios, adaptive energy-based processors (specifically MVDR) exhibit the most stable tracking continuity and lowest numerical peak errors. Simultaneously, the operational adaptability of subspace methods is improved via covariance matrix reconstruction (CMR). Specifically, the RCM technique effectively decouples unstructured sensor noise, mitigating maximum trajectory deviations and providing a balanced trade-off between computational efficiency and robustness. Statistical evaluations confirm the fundamental performance boundaries in static environments, while highlighting sample-size limitations in highly dynamic scenarios, thereby establishing a realistic, evidence-based benchmark for marine engineering applications.