Hi Cal,
> I would think that polys, points, & edges give you more
> control over details(?)
Well, they pretty much do! But the problem is that you end up forced to work on that "detailed level" much of the time, trying to manage a large sea of points and edges.
If the object that you are trying to build has a strong 2D profile element to it, the NURBS modeling method allows you to do a lot of work with 2D curves and then cut your object with those curves. This is a very fast way of working for the kinds of shapes that are suitable for this kind of a thing, which tends to include a large amount of mechanical or industrial man-made type shapes.
An easy way to see this in action is to just look through the video tutorials here:
http://moi3d.com/1.0/docs/tutorials.htm
Those give a good overview of how quickly you can create industrial structured kinds of shapes using NURBS modeling. Try building any one of those shapes in a polygon modeler and you will be spending a lot more time wrestling with those details to get your final result.
For things like Character models, faces, stuff that is organic with a lot of wrinkles and things like that, those are things where the detailed control of polygons is very well suited for and they don't map well to a 2D profile driven type workflow, so those are things that tend to work better in a poly/sub-d type modeling system rather than NURBS.
Neither method is the perfect tool for every single kind of model - and that shouldn't really be a big surprised because the field of modeling is incredibly vast!
For mechanical shapes in addition to speed NURBS also gives you a high degree of accuracy since booleans and cutting operations work much more effectively and also accurately with NURBS models rather than with polygons.
But like I mentioned, the best method really depends a lot on your current task at hand...
- Michael