OpenGL.
Both AMD and NVIDIA provide OpenGL extensions. (first vendor specific, and then as part of OpenGL if they are proven to work on both vendors).
Both companies are currently dedicated to bring OpenGL as close as possible to their hardware. Which makes sense. AMD might have a deal for next-gen consoles, but huge chunk of their market are still consumer level GPUs, and lets face the facts.
Microsoft is not really interested in improving graphics stack on Windows. If you want to play games buy Xbox. The amount of people that is using Windows for AAA gaming is neglible in grand scheme of windows sales.
And even if they were, they are not able of match the technology from AMD and NVIDIA. Due to time constrains and costs.
Actually the renderer API is less of the what Epic is using internally as:
- Mobile devices use OpenGL ES.
- Xbox one is using some varaion of DirectX
- PS4 is using libgcm
Of course replacing DirectX with OpenGL is huge task, that basically needs some huge code rewrite.
My bet is that is going to happen sooner or later. Solelely for the reason that OpenGL and OpenGL ES are more similiar than OpenGL ES and DirectX, and for second reason that Valve might succeed with SteamBox, SteamOS, or whatever they are doing right now.