What features should C# 4.0 onwards have to encourage switching from Java?
Make it run on as many platforms as Java?
Otherwise it is completely irrelevant to us.
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Edit: For a discussion about Mono making .NET "cross platform", see https://softwareengineering.stackexchange.com/questions/20275/mono-is-frequently-used-to-say-yes-net-is-cross-platform-how-valid-is-that
Edit 2015: Microsoft has decided to open source the backend part of .NET, which will enable community to port this to even more platforms than Java runs on. I consider this the ultimate move against the oracle approach to Java evolution.
Edit 2019: .NET Core is now available for Linux, and therefore as Docker images. Our experiences so far has been very nice. We have a mission critical application which runs nicely in Kubernetes, and we have no particular preference for writing microservices in either .NET or Java.
The general uptake of C# in the marketplace has nothing really to do with language features, which I understand are now superior to Java. Adopting C# requires a complete organizational strategic shift in the main:
You already have a gazillion Java applications and a host of Java developers. Why switch C#? You'll need new staff and suddenly all of your applications are legacy by definition. This is a huge deal! Undergoing this change puts a huge risk on your company for what may be only slight benefit: why bother?
You are used to at least the option of many large providers of operating system and middleware which support your Java ecosystem. This disappears overnight and you expose yourself to a monopoly pricing model (i.e. you are pretty much tied in to Microsoft, to all intents and purposes). Being subject to monopoly pricing is bad! Most organizations would rather have a slight technological disadvantage to avoid monopoly pricing because the pricing will almost certainly take away any extra revenues anyway.
I don't actually think that C# has anything less going on for itself than Java, except for the ecosystem like IDEs, frameworks, etc. In terms of features, it is well ahead at the moment at least.