I think you'll learn more from C++.
Java and C# are rather similar. They're both designed primarily for a certain kind of corporate environment. If you go from Java to C#, you'll spend most of your time picking up the .NET framework. The syntax will be different but you'll be doing the same thing in the same ways. (Don't get me wrong: those things are important and valuable -- you just don't want to pigeonhole yourself.)
I think that, as a novice, you'll benefit more from something less similar to Java. C++, C, or a scripting language could all fit the bill.
-- Alex