Where emulators are concerned, most are open source projects run by one or two people, as such they use OpenGL because DirectX isn't free and again they often just don't bother testing with AMD hardware since they simply don't own any. Thankfully most of the better emulators are moving to Vulkan for the same reasons they used to use OpenGL and AMD's GPUs are much better at Vulkan (in part because of Async compute which Nvidia's current GPUs have no real hardware support for and in part because AMD's mainstream GPUs have much more raw compute shader power for example the 1060 has 4.375 Tflops but the 580 has 6.175) Then of course you have the problem that AMD's GPU market share means that many small software companies and indie devs don't even bother to test their software on AMD hardware (same goes for Intel's CPU dominance meaning their IGP's get reasonable support, although that's changing) Plus Nvidia do stick their oar in A LOT with smaller devs going so far as to send teams to them to help 'optimize' their software for Nvidia GPUs, AMD just don't have the budget for this.

AMD have equivalents for many but they're not always supported well by apps. AMD's OpenGL drivers aren't bad exactly it's just that Nvidia's spend more money on it and of course Nvidia fully support all their own OpenGL extentions which a lot of OpenGL games and apps use.

Opengl 4.3 amd cards