The simple answer is: no, there is no direct alternative to OpenGL that is clearly superior. Direct3D is pretty much the only competitor of any kind, and although it is certainly competitive, it does not take any major advantage.
From time to time, Direct3D has an advantage in speed - it is controlled by Microsoft, which can quickly change the specification to take advantage of the latest graphics card updates. At that time, OpenGL was controlled by a multi-vendor (ARB) architecture review board. Decisions about new versions of OpenGL took a lot of time, and a significant number of vendors seemed to be more worried about backward compatibility than they took full advantage of all the new tricks as fast as the hardware manufacturers invented them (and nVidia and ATI are competitive enough to come up with , and quickly at the same time).
Since then, OpenGL management has been transferred to the Khronos group. There was some disagreement about the parts of what they did with the specification (in particular, the depreciation of many functions that quite a lot of people use), but one thing is open to a small question: now they revise new versions of the specification relatively quickly, so it provides access to functions even the latest equipment.
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