Is there any considerations to determine which is better practice for creating an object with private members?

var object = new function () { 
   var private = "private variable";
   return {
       method : function () { 
           ..dosomething with private;
       }
   }
}

VS

var object = function () {
 ...
}();

Basically what is the difference between using NEW here, and just invoking the function immediately after we define it?