Every time this question comes up, someone (usually me!) points out that feathering props are inherently less efficient than a well designed folder. Their basic design requires that the blades have no twist in their shape, ie they are flat paddle-like shapes, and this is by its nature inefficient. The bottom line is that it takes more engine
power to create a given amount of thrust; the most noticeable result is less fuel
They do generate lots of thrust in reverse when stalled, and thus are good for backing up off of mud banks and generating "braking" forces.
The better folding three blade props have gotten much better about thrust in reverse, but are not as good as a feathering one.
As Weyalan said, each has its benefits.