An age old battle rages between the proponents of softboxes and those for umbrellas.
I say, each has its place, depending on what you, the creative genius photographer wants to achieve.
The short video explains and shows the difference between lighting using a softbox and lighting using an umbrella.
Take a look at the video here.
The basic difference is that light from an umbrella is, in the words of Jean-Francois, "more contrasty"!
I just found a great little tool that allows you to turn an umbrella into a softbox.
It is called a "jellyfish". It is a translucent cover for your umbrella.
You can see it in action here.