The situation about those two API is greatly dependent of the PC game market which is completely dominated by microsoft.
You also have to understand that as the graphic technologies has been very much influenced by the progress made in computer speed, and since graphic acceleration involves all aspects of a computer (the electronic architecture aspect, the OS aspect, the CPU aspect, the API compatibility aspect), it involves a very tight and dense engineering work, so you can easily understand that it requires enormous resources so those technologies can not only be released, but evolve and be "easy" enough to work with for game and/or 3D engines developers.
Microsoft has been tightly working with nVidia, and they are more able to throw money to be sure their technology is more advanced on such special hardware, something which can't be possible with an open source model, since there are much less developers ready to work for an open model which doesn't rewards them money directly.
Open standards are been efficient for a long time but as this quote says:
"Walking on water and developing software from a specification are easy if both are frozen." Edward V Berard
The reason why it favors direct x is because shiny stuff sells more, and shiny stuff requires recent software AND hardware.
But you can still learn OpenGL, do something sufficient with it, and let the engines do the hard work, because graphic programming evolves a lot, and don't remember Direct X is not the only proprietary: Sony, Nintendo, and other Arcade or other systems, use proprietary APIs.
So my advice is this: learn OpenGL, because for the shiny stuff, you won't stay on OpenGL. You can also learn Direct X, but if you plan to work on consoles, you will have to learn again.
All that chit chat is not very interesting: just pick an engine like Ogre or Irrlicht or Panda3D and start coding.
And one thing: if you plan to learn either Direct X or OpenGL, be sure to learn everything you can about Matrix algebra, and some more which are specific to graphic programming.
The read will be long.