Because of the paper filter, you end up with a much smoother cup compared to brewing with a French press. Some prefer the heavy body and murky dark coffee flavor that you get from a French press, and while I do love a FP sometimes, I am more of a pour over guy myself.
Another favorite tool is the Hario V60, which is then same method as the Chemex but a different tool for getting the job done. (And the Hario gooseneck kettle is a MUST-have in any serious coffee drinker's kitchen.)
Check out the Chemex brewing method inside the Wild Foods Guide To Coffee HERE.