Well, I think the title and the image speak for themselves.
How come the Subsurf modifier doesn’t have a THIRD subdivision algorithm (other than Catmull-Clark and Simple), That acts the same way as subdivide smooth?
Why would you want to have a subdivide smooth-like algorithm in the subsurf modifier when it generally doesn’t handle smoothing an entire subdivided object at once very well, in fact the image above almost looks like a bug as the result would ideally be something similar to one or more subsurf iterations, not a object that looks padded (especially noticeable when setting the subdivide amount in the same operation a bit higher)
Meanwhile you could use the relax addon (bundled with Blender builds that come with the addons-contrib folder), it does a much better job when the iterations is set to the max amount.