XB1 uses a form of DX11 tailored to the HW/SW stack of the XB1.
The PS4 uses a form of OpenGL ES as its high level graphics API, but also sports a libgcm library for low-level HW access. For performance, using libgcm is preferred over PSGL.
So you are starting to create an ecosystem that looks like this:
Windows: Mantle, OpenGL, or DirectX
PS4: OpenGL ES (PSGL) or libgcm
NVIDIA: OpenGL or DirectX
AMD: Mantle, OpenGL, or DirectX
You are fast getting to the point where we are going to return to the days where different API's/Vendors support different feature sets. Remember the days where Glide offered the highest quality level, DirectX supported lower detail but higher resolutions, and OpenGL had the lowest resolution but advanced graphical features? We're going back to that. And that's not good for the ecosystem as a whole.
All this goes back to the failure to significantly update OpenGL back in the 2.0 days.