Deep learning has shown promising results for multiple 3D point cloud registration datasets. However, in the underwater domain, most registration of multibeam echo-sounder (MBES) point cloud data are still performed using classical methods in the iterative closest point (ICP) family. In this work, we curate and release DotsonEast Dataset, a semi-synthetic MBES registration dataset constructed from an autonomous underwater vehicle in West Antarctica. Using this dataset, we systematically benchmark the performance of 2 classical and 4 learning-based methods. The experimental results show that the learning-based methods work well for coarse alignment, and are better at recovering rough transforms consistently at high overlap (20-50%). In comparison, GICP (a variant of ICP) performs well for fine alignment and is better across all metrics at extremely low overlap (10%). To the best of our knowledge, this is the first work to benchmark both learning-based and classical registration methods on an AUV-based MBES dataset. To facilitate future research, both the code and data are made available online.