Hello,
It depends on your implementation, what do you plan on doing in the future?
The two languages are very much alike. C# and Java have almost synonymous syntaxes, so basically if you learn C#, you will know Java right off the bat. The only thing you will have to know is their API's (C# uses DotNet and Java uses java API). Of course, there also exists J# is java that also uses DotNet.
The two languages have their own purpose (as most languages do). Java was created back in 1995, by MicroSun. It's primary purpose was portability, and syntax simplicity derived from C++. In java, when a code is written it is compiled and run through a layer called Java Virtual Machine (JVM), so it is compatible across all systems alike without worrying about cross platform compatibility. It is so portable that you can even port it to web pages, and even mobile devices. However, with flash's advent, there are less of seen on the web. Developers also use java to do server-side programming as well.
C# is a language that is highly based on the syntax of Java and was created by Microsoft. C# takes syntaxes from java as well as C++. The C# community to date is enormous. However, C# is entirely based on DotNet, so when you learn C#, you have to how to use DotNet libraries as well. Other languages such as Visual C++, Basic, and Java use DotNet libraries alike. The DotNet libraries are becoming incredibly powerful, as is the Visual Studio IDE suite. DotNet has been extended to support mobile devices as well. C#'s primary use right now is largely for web development.
So, it depends primarily on what you want to do. In my opinion, both languages are so similiar that l woudn't even worry about deciding between them because you will eventually know both depending on how fast you learn your first language.
I'd say, learn C#, the IDE is incredibly user friendly and incredibly intelligent. C# is a very well documented language, each function has a little description that concisely details about what it does. Aside from all this, MSDN.net is basically dotnet's manual, it will document about every method that exists in DotNet. And if you want even more support, there is an enormous C# community all over the internet.