With sub-d you work with a subdivision surface - like a "smoothed" surface. With CPS you work with a polygon object, which you see smoothed certain times of your choice. You can go back and forth between these "smooth degrees". This gives you more control than sub-d.

Lets say you'd like to make a basic torso with a proxy, and afterwards model the details in regular poly. With sub-d - you must convert to poly. When you do so, the object will still be a "smoothed" version of the proxy. With CPS, you can delete proxy mesh and continue working on your model at whatever "level" you'd like. Lets say back to the proxy (no smooth) in this example.

In the picture - you can see the differents between the converted sub-d and the CPS (with deleted proxy mesh).

Theres other tools in CPS which ease your workflow, but this is the basic.

I hope this make sense.