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Deep learning based methods for automatic organ segmentation have shown promise in aiding diagnosis and treatment planning. However, quantifying and understanding the uncertainty associated with model predictions is crucial in critical clinical applications. While many techniques have been proposed for epistemic or model-based uncertainty estimation, it is unclear which method is preferred in the medical image analysis setting. This paper presents a comprehensive benchmarking study that evaluates epistemic uncertainty quantification methods in organ segmentation in terms of accuracy, uncertainty calibration, and scalability. We provide a comprehensive discussion of the strengths, weaknesses, and out-of-distribution detection capabilities of each method as well as recommendations for future improvements. These findings contribute to the development of reliable and robust models that yield accurate segmentations while effectively quantifying epistemic uncertainty.