Stacking the radiators will reduce their overall size because you then have to use less radiator tubing, smaller pumps and smaller radiator fluid tanks. Because the radiators are closer, the tubes can be shorter. In turn the pumps do not have to work as hard to pump the fluid over a shorter distance, which then allows you to use smaller and lighter pumps. Finally, you can use a smaller radiator fluid reserve tank, since your overall system is smaller and needs less fluid as a whole. Depending upon your overall design you may be able to reduce the amount of supports for the radiators by stacking them.
The cooling capacity increases on stacked radiators as opposed to a single radiator. Each radiator will allow for increased surface areas for the cooling system and more opportunities for the cooling fluid to transfer the heat to the outside air. If your radiator design is on a vehicle, you can stack the radiators at the front of the vehicle and use the forward motion of the vehicle to increase the cooling capabilities of the radiators. Relying upon passive cooling works, but for high temperature applications you need forced air flows (either through the vehicle accelerating or through the use of fans). By stacking the radiators, you can maximize the vehicle's own airflow or the airflow from a single fan.
Stacking radiators can come at a cost to efficiency as the radiators in the middle will have hot air from the other radiators going over their heat sink fins. That makes such a radiator far less efficient, since it will have to deal both with its own internal heat and the external hot air. It also reduces the amount of cool air the radiator can impart heat into and thus further reduces the radiator's efficiency.