At this time, you can make a pretty good living in either .Net or (the) Java (platform).
My research says there is a higher demand for Java programmers, with the potential that .Net may eventually be in higher demand.
As a beginner, it may simply come down to economics; most of what you need to learn and build Java apps is free (i.e. open source). The hard part comes in deciding what to use for what; e.g. choice of IDE (NetBeans, Eclipse); application server (JBoss, Tomcat); Web server (IIS, Apache), GUI (JSP, Faces, Tiles), etc.
With .NET its usually simpler: Visual Studio (VS) for the IDE; IIS for the Web and Application server (ASP.NET). You'll need to purchase VS; your clients need IIS licenses.
A choice of database isn't often a problem because most will work well with either project.
There is the "open-source" .NET route (the "Mono" project); this requires another evaluation and choice on your part.
In the end, you may very well be expected to be knowledgeable in both; even within the same company.
In general, I would say .NET is easier to learn (fewer choices); Java is cheaper to learn (open source); both are worthwhile knowing.