Advantages

The main advantage of radiosity is the realism of the result. Just throw a glance at the Blender Community Journal if you are not yet convinced.

Another advantage : solving the radiosity equation is viewpoint independant. Once you have computed the solution, you can change the viewpoint without having to recompute the solution. But, even the smallest movement of an object in the scene modify the energy exchanges, and you have to recalculate the solution.

That is why radiosity is perfect for domains where you have to render scenes with static objects, like architecture