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.
Of course, just as there are programmers who only code in C++, ASM, Cobol, Java and nothing else. It's a matter of preference. But even Yo-Yo Ma, I'm pretty sure, has played other instruments before settling on the cello.
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.
At this early stage, any performance benchmark doesn't matter. Why is he going to do now, write an algorithm computing 1 billion data points for secret military operations in Nevada? Think about it in utility sense. Java and C# are probably two languages that are the closest to one another in term of the syntax. The main differences between the two of them are the platforms they are typically used for. Now the question becomes which platform that the OP is most comfortable in. Choosing one does not mean that he's stuck at that for the rest of his life. Choosing C# does not mean "Oh no, Windows forever! Apple is getting popular! I can't switch anymore!" Choosing Java does not make you are a slave to JVMs. He can be learning C# now and switch to Java 2 years later, or vice versa. Can't you see how trivial choosing a language is, especially between C# and Java?