I've been developing in Java for almost ten years, and in C# for only a few months, so this comparison may not be as thorough as it could be. If I've missed something please feel free to comment.
Java is far more portable than C# for one. I've built applications on Windows, and ported them to Linux and Mac with minimal effort. With Android running on a Java-based platform, porting to Android is made far easier. There's no fussing with Mono and the like, no making sure you don't use any API functions that are only available in .NET.
Java also has a wide array of available IDEs with excellent features, and a huge, active community. There are libraries available for just about any technology you can think of, usually more than one, such that one of the options will likely fit your specific situation.
Java's runtime generics seem to be easier to learn and work with than C#'s compile-time generics; however, compile-time generics are likely better performing. Java's overridable-by-default scheme also makes development a lot easier in many cases. While I do understand the idea behind C#'s final-by-default scheme, I prefer a language that leaves those kinds of choices up to the developer rather than enforcing good development practices through language features.
The JVM is also now expanding to support other scripting languages, including PHP, Python, Ruby, Scala, and others.
C# has some excellent language features that I would like to see in Java, however. Extension methods are extremely useful for adding functionality to classes without having to subclass, particularly useful in adding functionality to library classes. C#'s delegate features are really excellent, and beat any workaround Java has for its lack of closures for callbacks and event handlers. The upcoming Java closure functionality looks like it will still pale in comparison to C#'s delegates.
LINQ is something I would love to see come to Java; the ability to query collections like databases is extraordinarily useful and eliminates a lot of tedious code iterating over collections. I've yet to use it for querying against a database, but it seems more than adequate for that purpose and likely much friendlier than JDBC. And while porting is more complicated, Mono is a very strong platform, and there's even a Mono module for hosting web applications through Apache.
Speaking of web applications, I have no experience so far with building web applications in C# .NET, but I have done some research. Based on that research, I have to say I significantly prefer JSP/JSTL/EL over ASP.NET. I prefer the syntax, the workflow, and JSP's tag library system over ASP.NET, which reminds me a little too much of PHP or old-school JSP (pre-JSTL/EL) for my tastes.
All in all, I can't say one is superior to the other; like any development decision, it comes down to which option is best suited to the situation and the developer. If you've had the opportunity to make that choice, please leave a note in the comments and let me know what you chose and why, I'd be happy to hear it!