Execution performance vastly depends on the concrete problem and its implementation. I do not want to give a general statement about the performance of the one compared to the other. In the past mono did tend to be a little behind the CLR. On the other hand mono has improved as well and now offers SIMD vector support (even if ILNumerics doesn't make use of it yet).
I suggest, you implement your solution and test it on several platforms / runtimes. I would be interested in your results as well!
One more note: mono can be used within Visual Studio as target platform. The Xamarin team offers a corresponding VS plugin. I haven't tested it though. Also, if you are into visualizations, keep in mind, mono favorites GTK over Windows.Forms. The ILNumerics visualization controls, however, use Windows.Forms. So you may have to install Windows.Forms on Linux manually.