Carbon fiber is carbon fibers woven together and cured in a resin. Fiber glass is glass fibers woven together and cured in a different type of resin. Carbon fiber is much, much stronger and lighter, but much more expensive and to cure it you must use an autoclave. Fiber glass cures at room temp once the resin is applied.
It depends on the application to decide which is better, but basically if you want to make a load bearing part out of one of these you use carbon, if you want to to make a part as light as possible, you use carbon fiber, if you want to be able to afford a non load bearing part at the sacrifice of a small amount of weight, you use fiberglass.