Preface: This is an honest question, not an attempt to start a "which language is better" war.
I'm proficient in C#. I haven't yet encountered any problems I can't solve with C# and the .Net open source ecosystem. (Perhaps that says more about the banality of the problems I'm solving than about .Net, but there you are.)
What would Rust give me the tools to do that I can't already accomplish with C# / .Net Core?