I think you mean "Bump Mapping" verses Displacement Mapping.
You need Mental Ray to do Displacement Mapping, but Bump Mapping can be done with both the Soft renderer and MR.
I don't have time today to write a desent desciption, but here is essentially the difference.
Bump mapping is an illusion created by changing the direction of suface normals based on the light and dark areas of a texture. ie: Light areas appear higher and dark areas appear lower. This illusion has problems at the edges of sufaces becuse only pixel colors of the object are changed to make the illusion and therefore the edge of the surface appears not to be effected. Regardless bump mappins is still sufficient.
Displacement mapping uses the light and dark areas of a displacement map to actually deform the surface in 3D space. Therefore, there is no issue around the edges.
A couple of other issues to consider. Bump mapping is not dependent on the resolution of the surface or polymesh. However, displacement mapping requires that the geometry to have sufficient resolution to handle the details needed. Therefore, the second method is much more costly in rendering times.
Urp