I would say this is entirely dependent on your use case. If you are running some simple web services in a cloud environment, it is generally cheaper to run them on a Linux system. Granted, if you are developing in .NET, you have probably already forked over some heavy cash for the development tools (Visual Studio, the OS, ReSharper, etc...)

The key trade off is deciding if it is worth it to sacrifice compatibility with certain libraries for the development speed and costs of not having to learn an entirely new tech stack for yourself or your team.

As for running ASP.NET on Mono, I believe that both are mature and capable enough of running in a production environment. The mono website has a page listing various companies using Mono (some with ASP.NET): http://www.mono-project.com/Companies_Using_Mono