In the picture below 2nd example is a simple round bevel, 3rd is a Sub-D, 4th is a NURBS. To my eyes I think that Sub-D converges to NURBS smoothness, but I am not sure if it is G2 or G3. What do you think?
Subdiv continuity & smoothness.blend (1.0 MB)
Yeah these seem different ways, on how the face normals are interpolated.
The most typical and standard normal interpolation that all 3D engines use is linear blend (aka Phong) because is the most simple and practical. It does the job and that’s it.
I think that in the case of Nurbs, since they are 100% mathematical and generated only from 4 points that various inaccuracies are introduced due to having more steps to perform until you get to the final shape that is rendered in the GPU. Compare this to a typical 3D mesh, that you get what you actually see, the real faces and the real normals, without changing anything the GPU renders it as it is.
As for example in Nurbs, you have the first level that calculates the surface, the second level calculates the normals, the third level is about getting the geometry sent to the GPU and rendered.
Is possible that in the case of Nurbs you have a little bit more variation compared to the real 3D mesh, due to having all of these steps to perform.
However changing the normal interpolation perhaps can give you some better way to “understand” the surface a bit better. No wonder why huge car manufacturers such as BMW do 3D prints of their cars in clay form and inspect them with eyes and touch. 3D normals and 2D screens are lying to us. 
Well it is proven, that Catmull Clark subdivision surfaces converge to a C2 continuous surface on regular points and to a C1 continuous surface at extraordinary points (e.g. points having a valence different than 4 - that is more or less than 4 connected edges). The original paper from 1978 already describes subdivision surfaces as “Recursively generated B-spline surfaces on arbitrary topological meshes”. A regular mesh converges to a bicubic B-spline and this is C2 continuous. At extraordinary points, the continuity is C1. For further insights and analysis of extraordinary points, you might also look into the paper by Jos Stam about evaluating points on the limit surface directly: https://www.researchgate.net/publication/2376828_Exact_Evaluation_Of_Catmull-Clark_Subdivision_Surfaces_At_Arbitrary_Parameter_Values
Well the zebra analysis in that specific test are similar. But you should also test more complex forms.
this is a cool video about splines continuity. she also talks about catmull rom splines but i am not sure if they use exactly the same interpolation as subdivision surfaces.
Does Sub-D converge to G3 continuity?
No it does not, or at least catmull clark definitely does not, as it has mentioned before its C2 for regular topo and can be just C1 otherwise. Btw. the continuity between nurbs-patches is also just guaranteed to be C2.
