I would like to diverge a bit from Xetick said, mainly about documentation.
Ok, it's hard to have nice documentation / tutorial for OpenGL (More again since all the old tutorials (like wonderful NeHe's tutorials) has been deprecated). But the advantages on DirectX is that you have full access to the specification of the API, on how it is working, why it has be done this way, how should react the driver. So, in fact, you have everything, but true, a bit pain in the ass to read it.
With DirectX, that's call, you have exemple ... plenty of tutorials ... but when you need something really precise ... no way to get it. I mean, last time I have tried to do differed shading ... the documentation (MSDN) looks oddly made to me, not enough precise information in it and ... I really didn't want to use the Dx10 effect files ... but all the tutorials are based on these strange files ...
So ... of course it's like you want, but from the documentation I have to said, I prefer a bit the painful OpenGL Specification explaining everything that the MSDN thing trying to hide me everything.
Now, a bit more about the APIs. OpenGL has the kind of advantages to implement extensions. Extensions are optionnal ... so you can have it or not. But at least, with extension, you can have something implemented even with no major version (not like waiting Dx12 to have something). Moreover, at some point extensions will be implemented in the core (if they are really useful

).
About pipelines. True they have really remove easy functions from OpenGL 1 (which allow us to get something drawing on screen quickly). But often ... it's still supported by the driver (I don't know until when, and I don't know if it will be forever ...). But in fact, they have done "the same" in DirectX10 where the fixed pipeline is also removed.
What does "fixed pipeline" removed?
Simply that the API will give you nothing to draw shapes on screen. So you will have to program the Graphic Card to get it properly on the screen. It brings us dynamic application and GC configuration ... but it also means that you have to do some more mathematics and work to get your first triangle on screen.
What else ?
Hum, I like OpenGL ES a lot. Actually, we are similar to -> OpenGL ES 1 -> OpenGL 1.4 / OpenGL ES 2 -> OpenGL 3 (I think)). OpenGL ES 2 has shaders (which is really cool feature trust me

)
OpenGL ES is a light version of OpenGL ... it means that some part has been removed but at least, it's cleaner.
OpenGL compare to DirectX doesn't give anything to load the textures / shaders ... which can bother some ... because you have to implement your own loaders.
OpenGL is compatible with multiple languages ... actually I am working with D ... but Java ; Python ; C# are the other possibilities. (I think that the C# thing is not the best for OpenGL ...)
OpenGL ES is used nearly everywhere now (apart PC and XBox games). Even the PS3 has a OpenGL ES implementation (but not a classical one, they have a lot of specific extensions to extend OpenGL). OpenGL ES is also on Android phones / iPhone iPad.
Finally I will conclude on support on PC.
This is a big point. OpenGL Drivers are often buggy (ATI more than NVidia ... Intel is so lame

). This is because the OpenGL consortium does not have a proper tests set and are not enough strict when according the OpenGL compliance. Microsoft is really stricter. So they have better drivers ...

And I think that's all

Thanks for listening