Ship detection algorithms in Synthetic Aperture Radar (SAR) imagery are broadly categorized into: (i) those that interpret sea clutter according to a pre-defined Probability Density Function (PDF), detecting anomalies in positions within the tail of the PDF based on a specified Probability of False Alarm (PFA); and (ii) those which utilize a sufficiently large training dataset to learn the decision boundary between the target and clutter classes. Despite numerous publications in both categories, a proper quantitative comparison of their performance is lacking. This study is a step towards crossing this chasm by conducting a direct comparison between two real-world representatives: (i) SUMO's K-distribution Constant False Alarm Rate (K-CFAR/SUMO) detector, and (ii) the Deep Learning Model that topped the xView3 (1 st DLM/xView3) challenge organized by the Defense Innovation Unit and Global Fishing Watch. The performance of both algorithms is characterized by tracking the number of False Alarms (FAs) and Missed Detections (MDs) in three labeled Sentinel-1A repeat-pass SAR images acquired in the Gulf of Guinea. The results demonstrate that 1 st DLM/xView3 outperforms K-CFAR/SUMO, achieving the best FAs-MDs trade-off.This paper is accepted for oral presentation in IEEE IGARSS 2024, Athens, Greece.