One thing I think the C# IDE will need to combat Visual Studio is a clean, and very intuitive UI. Now, I don't want to mash on any toes, but I personally found the IntelliJ UI to be very hard to get into. It just felt so overwhelming with options and features that I didn't want to learn to use it very much. I think that is one thing that Visual Studio has actually done right.
Microsoft is notorious for the mistakes they make, but rarely do they get much credit for the things they excel in. Visual Studio is one of few products that actually had a good, intelligent design behind it. The way things are laid out and organized provides a rather simplistic workflow, you don't have to spend very long learning the software, you can spend more time learning the language. I think this is absolutely vital in order to make a competing product.
My suggestion, at least, is that the IDE be very compact at the user's option. I'm not saying have a "Standard" and "Advanced" Layout, where one shows virtually nothing, and the other shows virtually everything, but instead things should be laid out in a manner of usefulness. For example, placing commands in the toolbar that are 'rarely used' would be rather non-sensical. Making too many menus is always cumbersome, but at the same time, sacrificing menus also sacrifices features. I dunno, just throwing in my two cents.