CPS emulates Maya's SubD. It is basically a form of smooth in Maya or 'Mesh smooth' (3ds max terminology). the cage is what you manipulate cut, delete, add and shape which then is followed through to the hi res mesh.
Maya's SubD has two modes. Standard and Proxy. Standard allows you to pull points, edges and faces directly and work in a hiarachical relationship with the different levels of points etc.. with the SubD.
Proxy mode is similar to CPS in that you are working with the lo res cage of the subD (which is a poly object) this mean that you can use all of the poly tools such as sculpt polygon tool, split polygon tool etc. But working in this manner is really slow. try it on a large, dense mesh.
When working in standard mode (of Maya SubD) it would be nice to be able to use the paint selection tool, but as far as I know it is not yet fully implimented. It only works to a certain degree and starts to select points not intended, etc...
CPS is nice because you can use all the poly tools, etc, they all work wonderfully. Also being able to use the sculpt polygon tool on one side of your character (a head for instance) and have a mirrored side created by CPS upate is really nice.
I will use Maya SubD's as a finishing tool to get extra detail using hiarachical function and for skinning and rendering. CPs is better (for me for the roughing out of a mesh).
Anyway have a play. I spend my time modelling between Maya, lighwave and Softimage. Each is easier to do certain things. The 'obj' format for poly's is a standard file import format for all of these programs.
Mayan elder......only in years.....