This paper introduces novel methods for comparing the accuracy of optical laser scanners. Moving beyond traditional deviation-based comparisons, it explores the use of shape functions to measure distances, cone heights, and curvatures, aiming to provide a more comprehensive assessment of scanner performance. The processed data is in the form of point clouds that can be organised into the triangular meshes and can represent the surface with the given inaccuracy of the scanner.Meshes of special surfaces (such as sphere or ball bar) are used for the scanner calibration, qualification and verification. The research employs three types of laser scanners with varying accuracies and analyzes the results of their accuracy using both established and new methodologies. Measurement system analysis is used to verify that these functions can be used for scanners comparison. The comparison of shape distributions obtained from results of shape functions in the form of polylines was used to compare scanners according to their accuracies. Results demonstrated that shape distribution in the form of polylines is an effective way to compare scanners based on accuracy. This method can be used in a wide range of applications and can be used for laser scanning.