The answer to this is probably somewhat subjective depending on what environment or platform you are using. My approach is usually to look at the project and choose what works best for each situation. Generally, I lean towards .NET for ESRI based projects and Java for open source / other solutions. My experience has been that as long as you know how to program in general, it’s not so much the language or syntax that slows you down, it’s learning the different APIs and getting them to do what you need.
In your case, if you know what platform you’ll be using or would like to use, concentrate on the language that best fits. Java and .Net are both widely used in the industry and have a lot of support for getting started. Also, Java and C# for .Net are somewhat similar syntactically, so starting with one over the other won't necessarily hurt you and could allow you to switch over down the road with a smaller learning curve if your needs change.
My two cents.