Ultimately, Java or C# or C++ do not matter. You really should consider programming languages as musical instruments, and you use them to play your music. Some instruments work better for certain types of music. But just like any other good musicians, a programmer must learn how to play not just one instrument, but several. Depending on what music he wants to play, what mood he wants to convey, he picks up the right instrument and play it like a maestro.
It seems like musicians have a speciality though like Yo-Yo Ma.
Since you are a beginner, pick one. Java or C# really does not matter. C# has XNA for games. Java, on the other hand, has plenty of 3rd party libraries, but also allows you to make games for Android. Pick your platform (XNA or mobile), then start learning.
Picking one makes sense, but I think the decision matters and depending on the person could see them deciding to focus on C# or Java. If I were forced to pick between those two I think I'd pick C#. The performance of this compression library on different languages is kind of interesting.