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Estimating neuron location from extracellular recordings is essential for developing advanced brain-machine interfaces. Accurate neuron localization improves spike sorting, which involves detecting action potentials and assigning them to individual neurons. It also assists in monitoring probe drift, which affects long-term probe reliability. Although several localization algorithms are currently in use, the field is nascent and arguments for using one algorithm over another are largely theoretical or based on visual inspection of clustering results. We present a first-of-its-kind benchmarking of commonly used neuron localization algorithms. We assess these algorithms using two ground truth datasets: a biophysically realistic simulated dataset, and an experimental dataset pairing patch-clamp and extracellular Neuropixels recording data. We systematically evaluate the accuracy, robustness, and runtime of these algorithms in ideal recording conditions and long-term recording conditions with electrode degradation. Our findings highlight significant performance differences; while more complex and physically realistic models perform better in ideal conditions, models relying on simpler heuristics demonstrate superior robustness to noise and electrode degradation, making them more suitable for long-term neural recordings. This work provides a framework for assessing localization algorithms and developing robust, biologically grounded algorithms to advance the development of brain-machine interfaces.