The brush tool has an entire window of control sliders and options to change and alter the brush (best used with a wacom tablet or cintiq) based on the tilt, rotation or pressure of your digitizer pen. The shape, opacity, size, scatter, texture, etc can all change depending on how you set up the tool and how you use the pen/tablet.
The pencil tool is a solid pixel by pixel tool. It does not anti-alias (or fade or have fuzzy edges on the lines). You can change the size (or number of pixels) and color of the tool.
Basically, the pencil tool will give you an 8bit look and the brush tool will give you a painted look (depending on the settings you choose)