You're better off choosing one or the other. Companies that are looking for Java people don't care how much .Net you know, and for companies looking for .Net people, Java is merely expensive coffee.
I'm not sure what the comparison for jobs is right now, but off-hand I'd say they're roughly even, with Java having a small advantage.
Just remember, if you go Java, you'll have to learn a whole truck-load of additional technologies and frameworks. Nobody hires a "java programmer" anymore, you need to know J2EE, JSF, Junit, Spring, Hibernate, and lord only knows what else.
With .Net, you'll need to know C#, Sharepoint, SQL Server, and other Microsoft technologies.
So your choice pretty much comes down to how much you like or dislike Microsoft and their products. Dislike them, stick with Java. Like them, stick with .Net.
EDIT: Poster Jason has some good advice about checking CareerBuilder dot com. I thought I'd add to that, Dice dot com, Monster dot com, and JustTechJobs dot com. I use Dice all the time, especially since it's geared towards technology jobs, but when you're job-hunting it's a good idea to use as many resources as you can.
In particular, you can go to Dice and search for keywords, and count how many hits. E.g., right now it has about 18000 hits for Java (out of 87000 total jobs), and about 11000 for .Net. That's a very shallow measurement -- you should also consider things like location and whether they're looking for junior or senior people. But you can always used advanced search, and you can read some of the job descriptions.
Good luck!