Neither really hold a strict advantage over the other. In terms of platform support there's a good deal of market-share/revenue-potential overlap, but also exclusive support for certain platforms in either camp -- For example, if you want to run your game on XBox One, Windows RT (Surface, et all), or Windows Phone, you need to support Direct3D; likewise, basically every other platform runs OpenGL or OpenGL ES -- Although "more platforms" is a decent enough argument in favor of OpenGL, in practice the D3D ecosystem is probably about equal to the GL-based ecosystem in terms of dollars (if not users) available, but the GL-based ecosystem is more fragmented (linux, MacOS, iOS, Android for starters, and myriad hardware devices to finish) so its more work to tap all its potential. In the D3D-centric ecosystem, you can reasonably ask for more money for your game, whereas the bulk of the GL-based ecosystem is iOS/Android, where you reasonably can't and have to design around and subsist yourself on micro transactions for the most part. Anyways, none of this money stuff might be a concern for you now, but its worth bearing in mind for the future.
Other than that, Direct3D is a little more "modern" in its features and syntax (for better and for worse), but the two are close enough in functionality that you can create an abstraction layer between the two without much trouble. Pick one and learn it using contemporary best-practices, and all will be fine.
Edited by Ravyne, 16 December 2013 - 04:30 PM.