While there's nothing you can do in C# that cannot be done in F#, the reverse is not true. The biggest thing that comes to mind is to influence the direction of the other language (C#). I've heard it said many times that if you want to see what features will be in C# in the future, look at F#. Too many features to cite (though Linq is the biggest that comes to mind) were in production use in F# long before they arriv…
Thankfully F# and C# mix so well together I could've written a quick C# project to do it if needed, but I didn't want to break up my F# project into two + some C# glue
In the vast majority of cases though what you said is true. Discriminated unions, records, computation expressions, and type providers are total game changers