And even then, .NET isn't an alternative to JEE. It's a lot broader. .NET is an alternative to the entire
Java platform, JSE, JME, AND JEE.
I fear that the move to open source the platform will indeed mean that Java will soon enter a decline.
Whether .NET will benefit from that or not remains of course to be seen, it might well be that some other technology instead takes it place, like Python or Ruby (which are available on more platforms than is .NET, important for people/companies employing non-Windows server architectures with Java applications).
But at the moment I don't see any strong move in progress away from Jave and towards .NET. There is some drift, but that goes both ways (and quite a few people happily use both together).