Is there any performance different between hosting your asp.net in mono on linux and iis on window server?
Of course there is a difference, just like there is a performance difference between Java and .Net. However, it is going to vary widely based on what the application is doing.
There are things where .Net is much faster than Mono. There are things where Mono is much faster than .Net. There are things where they perform roughly equal. The same holds true when comparing applications running on Windows or Linux. The same holds true when comparing applications running on IIS and Apache.
Likely, either can run your application fast enough, and you will find that your performance is going to be driven by your programming techniques. The difference of a few requests per second probably isn't a huge issue unless you have a large server farm, in which case you most likely have the resources to test on both and see which is faster for your particular application.