General benefits of functional programming over imperative languages:

You can formulate many problems much easier, closer to their definition and more concise in a functional programming language like F# and your code is less error-prone (immutability, more powerful type system, intuitive recursive algorithms). You can code what you mean instead of what the computer wants you to say 😉 You will find many discussions like this when you google it or even search for it at SO.

Special F#-advantages:

Asynchronous programming is extremely easy and intuitive with async {}-expressions – Even with ParallelFX, the corresponding C#-code is much bigger

Very easy integration of compiler compilers and domain-specific languages

Extending the language as you need it: LOP

Units of measure

More flexible syntax

Often shorter and more elegant solutions

Take a look at this document

The advantages of C# are that it’s often more accurate to “imperative”-applications (User-interface, imperative algorithms) than a functional programming language, that the . NET-Framework it uses is designed imperatively and it’s more widespread.

Furthermore, you can have F# and C# together in one solution, so you can combine the benefits of both languages and use them where they’re needed.