This class has this description:
Provided for backward compatibility with ASP.NET MVC 3.
And the source is just:
public abstract class AsyncController : Controller
{
}
I can´t find any documentation about deprecation of this class at MSDN. Should I replace uses of AsyncController to Controller?
No.
Yes, asynchronous actions are implemented in new way in asp.net-mvc 4, using Task Class
More reading at Using Asynchronous Methods in ASP.NET MVC 4