I have used both charcoal and graphite for art projects. I have personally never combined the two in a single project.
Charcoal is generally much darker, bolder and messier. It's easy to fade charcoal or wipe it off the paper entirely if you make mistakes. Charcoal, due to its brittle nature is also easy to smudge or gently wipe to assist in your shading efforts.
Charcoal artwork needs to be treated after you're finished with the work as the particles (essentially dust) will fall from the artwork over time and may either leave dark streaks on the artwork or just cause the art to fade as the particles fall over the art or off of it all together.
Graphite is a slightly harder to shade with, and doesn't usually get as dark as charcoal. Some of the darker graphites, like an 8B, tend to look glossy and reflective when used over large areas. This is something charcoal does not do.
Graphite can be easily shaded with the help of tortilons, though, and varying pressure in combination with pencil grades can give you a very wide range of shades to work with. Graphite also lasts on the paper without particles falling off and can remain in-tact for years as long as its not being touched or rubbed.
The paper you use plays a big role on the art itself. Some papers, like newsprint are great for quick charcoal sketching and practice. Charcoal easily wipes from newsprint and it's cheap, while graphite is hardly visible. Higher quality papers are less forgiving of errors, but the finished product will look nicer.