[jquery] Should I use .done() and .fail() for new jQuery AJAX code instead of success and error

I have coded like this:

$.ajax({ cache: false,
    url: "/Admin/Contents/GetData",
    data: { accountID: AccountID },
    success: function (data) {
        $('#CityID').html(data);
    },
    error: function (ajaxContext) {
        alert(ajaxContext.responseText)
    }
});

But when I look at the jQuery .ajax() documentation at the end it seems to suggest I should be coding like this below or at least it suggests adding a .done() and a .fail():

var request = $.ajax({ cache: false,
    url: "/Admin/Contents/GetData",
    data: { accountID: AccountID }
});

request.done(function (data) {
    xxx;
});
request.fail(function (jqXHR, textStatus) {
    xxx;
});

Update

If I code like this is it the same or is there some advantage to breaking it into three ?

$.ajax({ cache: false,
    url: "/Admin/Contents/GetData",
    data: { accountID: AccountID }
}).done(function (data) {
    xxx;
}).fail(function (jqXHR, textStatus) {
    xxx;
});

In simple words

$.ajax("info.txt").done(function(data) {
  alert(data);
}).fail(function(data){
  alert("Try again champ!");
});

if its get the info.text then it will alert and whatever function you add or if any how unable to retrieve info.text from the server then alert or error function.

When we are going to migrate JQuery from 1.x to 2x or 3.x in our old existing application , then we will use .done,.fail instead of success,error as JQuery up gradation is going to be deprecated these methods.For example when we make a call to server web methods then server returns promise objects to the calling methods(Ajax methods) and this promise objects contains .done,.fail..etc methods.Hence we will the same for success and failure response. Below is the example(it is for POST request same way we can construct for request type like GET...)

 $.ajax({
            type: "POST",
            url: url,
            data: '{"name" :"sheo"}',
            contentType: "application/json; charset=utf-8",
            async: false,
            cache: false
            }).done(function (Response) {
                  //do something when get response            })
           .fail(function (Response) {
                    //do something when any error occurs.
                });

I want to add something on @Michael Laffargue's post:

jqXHR.done() is faster!

jqXHR.success() have some load time in callback and sometimes can overkill script. I find that on hard way before.

UPDATE:

Using jqXHR.done(), jqXHR.fail() and jqXHR.always() you can better manipulate with ajax request. Generaly you can define ajax in some variable or object and use that variable or object in any part of your code and get data faster. Good example:

/* Initialize some your AJAX function */
function call_ajax(attr){
    var settings=$.extend({
        call            : 'users',
        option          : 'list'
    }, attr );

    return $.ajax({
        type: "POST",
        url: "//exapmple.com//ajax.php",
        data: settings,
        cache : false
    });
}

/* .... Somewhere in your code ..... */

call_ajax({
    /* ... */
    id : 10,
    option : 'edit_user'
    change : {
          name : 'John Doe'
    }
    /* ... */
}).done(function(data){

    /* DO SOMETHING AWESOME */

});