The main benefit of the Marching Cubes algorithm is that it produces high quality images, due to the algorithm placing high importance on preserving as much of the original data and structure.
The images produced have high levels of detail, and thus can be displayed well at high resolution. The main reason for this is that Marching Cubes generates sub-voxel sized facets, yielding detail on the scale of at least voxel dimensions.
The connectivity information between slices is preserved, that is, the top and bottom faces of voxels carry as much significance as the other faces, avoiding possible anti-symmetry. This is in contrast to techniques such as contouring slices followed by tessellating between slices, which exhibit this problem.
Importantly, the gradient information of the original data is preserved in the normal vectors of the vertices. While normal vectors could easily be calculated from the created triangle mesh and used for shading, the algorithm instead opts to use information from the dataset to generate these normals. The result is that the normals may not indeed be normal to the corresponding faces, but are more accurate when used for shading as they are based on the original data, not the triangle approximations. This makes more attractive images with better shading.
Finally, the algorithms divide and conquer approach is well suited to parallelisation, where this may be desired in an implementation.