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Here you have a test with DX11 scores and opengl scores: http://www.sweclockers.com/recension...850/7#pagehead
I think they are quite close in performance. However I think Nvidia and AMD spends more time on optimizing direct3d than they do with opengl because that is what most games currently use on the PC platform.
The core code is likely identical in terms of acceleration.
The differences between GL and D3D for performance stem from GL's state model, the difficulty of threading it properly, and the extra checks that have to be run on many object uses because of the highly mutable object model. The latter at least is being slowly fixed with each successive version of GL (e.g., ARB_texture_storage), but has a long way to go. The threading problem cannot be fixed without literally scrapping and redesigning the API, as the fundamental problem is that the API expects and requires magic global hidden state (which can be thread-local, but that is not free), and in the short term requires scrapping and redesigning WGL and GLX (the changes from GL3 made it much better, but still far from perfect). The GL state model is just utter shit and needs to be shot in the face six times with a high-powered rifle; there's no fixing it, simply throwing it away and starting over. The API is simply trash, and even Khronos knows that fact (hence the Longs Peak fiasco). They just aren't willing to do anything about it; they introduce things like Core profile that break back-compat in little minor ways that barely affects anything at all while refusing to just introduce a revised API that breaks things in larger but actually useful ways.
The biggest problem with GL as an app developer is that -- on Windows -- the drivers are simply buggy and unstable. I still run into frequent driver crashes or just crazy performance problems that are simply bugs. The problems usually get fixed (though a few really bad long-term bugs haven't been fixed even after two years on NVIDIA's drivers) eventually, but the releases that fix one set of bugs inevitably just cause more.
Don't even get me started on what a horrifically bad shading language GLSL is, either. It's only just becoming sane with GLSL 4.20, which means you can't actually use any of its features since most of us need to target GL 3.1 hardware (Intel) or GL 3.2 operating systems (OS X) or just stick to GLSL|ES 2.0 (iOS, Android, NativeClient).