[newsit]

Learn both. Seriously. Pick a good book about algorithms or data structures, open Visual Studio and Eclipse, load the Java and .NET docs in your browser, maybe pick some introductory books on both and start coding the examples. It might take a little longer to start, but it will pay out tremendously in the end.

I've been doing this with Scheme and Erlang using SICP (http://mitpress.mit.edu/sicp/) and it has definitely helped me understand better both the languages and the material.

In your case you have two very similar platforms, object-oriented, garbage collected, with a very similar syntax. The big strengths for both are their libraries and their VMs, learning them in parallel makes lots of sense.