Given the following code:

public class C
{
    public void M()
    {
        var x = 5;
        Action<int> action = y => Console.WriteLine(y);
    }
}

Using VS2013, .NET 4.5. When looking at the decompiled code, we can see that the compiler is caching the delegate at the call site:

public class C
{
    [CompilerGenerated]
    private static Action<int> CS$<>9__CachedAnonymousMethodDelegate1;
    public void M()
    {
        if (C.CS$<>9__CachedAnonymousMethodDelegate1 == null)
        {
            C.CS$<>9__CachedAnonymousMethodDelegate1 = new Action<int>(C.<M>b__0);
        }
        Action<int> arg_1D_0 = C.CS$<>9__CachedAnonymousMethodDelegate1;
    }
    [CompilerGenerated]
    private static void <M>b__0(int y)
    {
        Console.WriteLine(y);
    }
}

Looking at the same code decompiled in Roslyn (using TryRoslyn), yields the following output:

public class C
{
    [CompilerGenerated]
    private sealed class <>c__DisplayClass0
    {
        public static readonly C.<>c__DisplayClass0 CS$<>9__inst;
        public static Action<int> CS$<>9__CachedAnonymousMethodDelegate2;
        static <>c__DisplayClass0()
        {
            // Note: this type is marked as 'beforefieldinit'.
            C.<>c__DisplayClass0.CS$<>9__inst = new C.<>c__DisplayClass0();
        }
        internal void <M>b__1(int y)
        {
            Console.WriteLine(y);
        }
    }
    public void M()
    {
        Action<int> arg_22_0;
        if (arg_22_0 = C.<>c__DisplayClass0.CS$<>9__CachedAnonymousMethodDelegate2 == null)
        {
            C.<>c__DisplayClass0.CS$<>9__CachedAnonymousMethodDelegate2 =
                            new Action<int>(C.<>c__DisplayClass0.CS$<>9__inst.<M>b__1);
        }
    }
}

We can now see that the delegate is now lifted into a private class inside C, a similar behavior that we're used to seeing when closing over an instance variable / field (closure).

I know this is an implementation detail which may be subject to change at any given time.

Still I wonder, what are the benefits of lifting the delegate into a new class and caching it there over simply caching it at the call site?

Edit:

This issue talks about the same behavior as asked here.