Func/Action vs. local functions

Question

With C# 7 we get the feature to define local functions:

private void Foo()
{
    string myString = getMyString();

    string getMyString()
    {
        return "Hello SO!";
    }
}

Is there a benefit or drawback to using this over Func<> or Action<>?

private void Foo()
{
    Func<string> getMyString = () =>
    {
        return "Hello SO!";
    };

    string myString = getMyString();
}

I'm only talking about using the function inside of Foo. Of course when I want to pass the function around I need to use Func<> or Action<>, but when I only want to use it in this scope is one of those ways superior over the other, and if so, how?