This paper describes a novel experiment in which two very different methods of underwater robot localization are compared. The first method is based on a geometric approach in which a mobile node moves within a field of static nodes, and all nodes are capable of estimating the range to their neighbours acoustically. The second method uses visual odometry, from stereo cameras, by integrating scaled optical flow. The fundamental algorithmic principles of each localization technique is described. We also present experimental results comparing acoustic localization with GPS for surface operation, and a comparison of acoustic and visual methods for underwater operation.