Disclaimer: I've done some work in both environments, but I definitely have more experience and in-depth knowledge in the .NET arena.
I'd say the stacks have many similarities, and their overall direction seems to plot along with the general direction of computer science as a whole. For example, both have been adding VM capabilities to support dynamic languages lately, which has allowed for dynamic languages to start showing up on both platforms.
What's most different is the ecosystems that surround the platforms. Java's community is largely open-source driven and while major commercial entities still actually push the platform forward, it's at least a consortium of them, instead of a single company driving the platform like in the Microsoft space.
Because the OSS community is so prevalent in the Java space, the Java stack typically moves forward with new ideas a bit faster than .NET. Things like dynamic languages on the Hotspot VM and even old technologies like web frameworks employing MVC are typically much farther along than they are in the Microsoft world. That's not to imply that .NET doesn't have successful OSS projects, but many of the most popular are in fact ports of Java projects (NHibernate, Lucene.NET, etc). Additionally, a lot of the .NET advocates and experts are the Microsoft MVP crowd who make a living selling books and speaking engagements and typically track along with Microsoft product roadmaps. I'm not arguing that they are all shills for the company, but simply that innovation in the .NET ecosystem that doesn't come from Redmond is much rarer than it is in the Java space.
So, while you could argue that learning Java syntax may not be worth the time (since it's so close to C# in so many cases) I find it personally rewarding to keep up with the Java community (as well as others, like Ruby) as it's one way to glimpse the future and generally make you a better developer. Even if you're not writing Java code but simply paying attention to Java podcasts or blogs, you're likely to learn some new technique or technology that may prove to be relevant.