This paper compares two mesh-based curvature reconstruction methods that have been tested both on analytical and camera-acquired meshes of simple solids. The comparison involves one linear and one quadratic fitting method, for which the asymptotic error behavior between the theoretical and computed values of curvature is numerically assessed using progressively refined meshes of the same geometries. Different methods for computing the normal and constructing appropriate sets of neighbors at a node are also compared. Results show that even though the quadratic reconstruction method exhibits a better convergence rate than the linear method, precision of both methods is highly dependent on the chosen node neighbor set. For simple surfaces and meshes that are not too dense, the linear fitting method is quite competitive with the quadratic both in terms of of precision and computation time.