Displacement mapping is very different from Bump Mapping.
Bumpmapping is an illusion. it creates relief on a flat shape using a special way to compute illumination of each pixel of the shape. There are different technics to create Bump mapping: Emboss Bump Mapping, dot3Bump mapping, Parallax Bump Mapping, Relief Mapping, ... The last technics recquire shaders for real time rendering.
Displacement mapping move each vertex in the direction of its normal, in a distance which depend on the color of the texture on the vertex. It do not recquire Shader, DirectX 11 or OpenGL 3.1. It can be done with CPU. This feature was already available on 3DS Max 1.0 and maybe also before.
Hardware displacement mapping is a way to create displacement mapping in real time using shaders. It is also already available on DirectX 9 and OpenGL using shaders.
I think Hardware Displacement mapping would be less usefull than "CPU" Displacement Mapping.
Displacement mapping is not better than Bump Mapping because it recquire more vertices and faces ("to move"). It's just different.