Why should I choose
ASP.NET Application (.NET Framework)
ASP.NET Core Web Application (.NET Framework)
Although both project templates use Full .Net Framework, Option 1 is for creating projects using legacy version of ASP.NET MVC in which we can use Global.asax.
Option 3 is totally new concept in which wwwroot folder, using task runners and everything is through OWIN middleware.
A lot of organization and companies are not ready to jump into new project template yet. I believe Option 1 is there for backward compatibility.