First implementation of the boolean operations on Brep models where done on polyhedral approximations. This was called Facetted modelers. The approximation can be constant or toleranced based. Last generation of facettized modelers keeps the original surface information on each facets but it does not prevent the system to have an erroneous topology. 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.