Use of surfaces instead of facets leads to higher complexity. Computations are complex and based on high level surface intersection. In a Voxel based system the material is represented by a succession of small cubes like an image is represented by pixels on your screen. The precision of the scene is the size of the voxel. The more voxel you have the more precise but also the expense of memory and computation increase.
Some systems increase their performance by supporting a system of hierarchically subdivided cells.
This approach is very good for imaging purpose or fast clearance checking. No analytic definition of faces or surfaces. Both are correct.