according to maya:
nurbs
NURBS stands for Non-Uniform Rational B-Splines.
• Non-Uniform refers to the parameterization of the curve. Non-Uniform curves allow, among other things, the presence of multi-knots, which are needed to represent Bezier curves.
• Rational refers to the underlying mathematical representation. This property allows NURBS to represent exact conics (such as parabolic curves, circles, and ellipses) in addition to free-form curves.
• B-splines are piecewise polynomial curves that have a parametric representation.
polygons
A polygon is an n-sided shape, defined by its corners (vertices) and the straight lines between them (edges). When you model with polygons you usually use triangles or quadrilaterals ("quads"), although Maya supports polygons with more sides. An individual polygon is often called a face, and is thought of as the filled area defined by its vertices and edges.
subdivisions
Modeling with subdivision surfaces is an easy way to create intricate objects such as human hands. It combines the best features of NURBS and polygonal modeling.
Subdivision surfaces allow you to use a single surface to model complex shapes. A single subdivision surface can have different levels of detail in different regions. That is, a region that has a complex shape can have more control points to allow finer detail, while a simple or flat region needs fewer control points.
How it works
Subdivision surfaces get their name from this dividing into regions of greater detail. You start with a base mesh and divide and subdivide regions into finer and finer detail, with each subdivision giving greater control in that area.
You reshape subdivision surfaces by modifying control points at the different levels of the hierarchy. The base mesh (or "level 0" mesh) allows you to reshape large areas of the overall surface. The subdivided levels allow finer control in specific regions of the surface.
Advantages
• Subdivision surfaces allow higher level control over shape than polygons.
• They allow you to only use complex geometry in the complex regions of your model.
• They allow creases (sharp edges) and arbitrary topology (not just four-sided sheets).
• The continuity of subdivision surfaces eliminates many of the problems that can occur at seams when you animate NURBS surfaces.
• You can bind subdivision surfaces to skeletons at a coarse level and the effects will translate smoothly to the finer levels.
according to me:
nurbs
pros
• good for surface modelling
• easily translatable into other programs
• good output for cnc milling
cons
• surfaces are often difficult if not impossible to attach
• not good for 3d printing
• usually require lots of rebuilding
polygons
pros
• easier to work with then subdivisions
• easy to attach
• can be modelled as a single, continuous surface
• good for 3d printing and cnc milling
cons
• lacks the level of detail available in subdivisions
subdivisions
pros
• can get into an amazing level of detail
• good for 3d printing and cnc milling
cons
• cannot be redered with mental ray
• difficult to attach and duplicate