That is a question no one in the whole word can answer it for you... not even google can. you can use google and start sailing in the large oceans of opinions and flamewars and still you wont get a direct answer.
for me I have never used OpenGL, but graphics look the same for me as these video show, both produce pretty visuals.
so for graphics beauty there will be no noticeable differences between them, at least from the players perspective. even thought some results from google says that OpenGl has more features such as Two-sided lighting, picking, ....etc.
however if you are a good programmer you are most likely to find ways around limitations. or implement them in your game (e.g. implementing a picking mechanism in a directx game).
so I think performance and ease of use now are the things that you should be concerned about.
performance depends on how the driver was made for OpenGL, since OpenGL drivers do the resource managing (e.g. moving texture data from VRAM to RAM when low on VRAM) so 2 games written using both directx and opengl might switch places when you run them on different systems.
Directx gives you the ability to choose what type of resource managing you want when you create the textures... you can use D3DPOOL_MANAGED to automate the process. or you can use other options listed here
for ease of use, for both Directx and openGL, you can view the code provided in the http://www.rastertek.com/tutindex.html
tutorials that i linked earlier (link contain openGL tutorials too) and decide for yourself or maybe wait for someone who used both libraries and can tell you his opinion on which is easier.
look here... this might help you decide.
also as the guys before me said or pointed to platform support should also be one of you considerations.
Directx ==> only windows (other operating systems might be able to run your game using wine / not free)
OpenGL ==> multi-platform which means more audience