Personally I'd say .NET, but I've got a windows development background.<p>On many angles (open-source project count, speed of most-optimized code, etc) I think Java is clearly ahead - however on many other angles, I think .NET wins.<p>C# is a much nicer language to program with, having all kinds of nice things like type inference, async/await, generics that work properly, proper closures, anonymous types, LINQ, and other things that Java doesn't have, and probably never will.<p>I also think the memory and disk footprint of a .NET server application is likely to be a lot lower than that of Java - In my company we have some REST api's written in C# running on windows, and some comparable REST api's written in java, and the C# ones consume about 100MB of RAM compared to over 1GB for the Java ones. The java programmers tell me this is a side effect of the open source project culture - A typical .NET service might pull in half a dozen third party libraries whereas a java service might pull in dozens.<p>.NET Core running on linux I find to be <i>really</i> interesting - it's just as fast as the windows one, if not faster, and uses a comparable amount of memory (I.E. still heaps less than java) - I'd go with that if I were starting today. Yes it's very new, but remember the core parts have been battle-tested in .NET for windows for over a decade, so it's not <i>that</i> new.
Also if you're developing a big new enterprise system I'd guess your timelines are in the multi-year range. .NET core is going to have a long time to mature before you need it for production critical systems.<p>Looking further ahead, to be honest I like the look of .NET more than Java as well.
C# 7 ships very soon with a bunch of nice language level features, and microsoft are really pushing forward with .NET core and making a lot of improvements. Java on the other hand is moving a lot more slowly, and since Oracle purchased sun there has been a lot of noise in the java OSS community about Oracle abandoning large parts of it and basically letting it fall to bitrot.<p>P.S. As much as I like Visual Studio, IntelliJ is a lot better... Just make sure you've got heaps of RAM :-)