The advantage of a closed loop is that its a good way to provide extra flow in the tank by the use of an external pump. The closed loop is setup with supply lines from the tank well below the water line and the supply line runs into the intake of the pump and then the outlet from the pump runs directly back into the tank to provide water movement. The difference between a closed loop and a sump setup is that the closed loop is just as its named. Its a totally closed system where as the sump would be an open system where you can add and remove water. In the closed system everything is enclosed in plumbing with no real access to add/remove water from the system.
Disadvantage is that you need to have bulkheads installed in your tank to permit the supply and return lines as you cant really use a hang on overflow for a closed loop as the potental for introducting air into the closed loop.