Is PHP faster than Nginx/Apache to check file exist?

I need to check the availability of a file on the server and then doing some reaction related to the file. I have the file name and path in each client and server side, then I have two ways to check the availability. One from the client side and another one from the server side.

First way:

Client side:

function check_file()
{
    $.ajax({
        url:'http://www.example.com/somefile.txt',
        type:'HEAD',
        error: function()
        {
            //file not exists
            //check again after 5 seconds
            setTimeout(function(){
                check_file();
            }, 5000);
        },
        success: function()
        {
            //file exists
            //start doing other actions related to the file
            action_1();
        }
    });
}

function action_1()
{
    $.ajax({
        url:'http://www.example.com/action_1.php',
        success: function(data)
        {
            var result = $.parseJSON(data);
            if (result.success)
            {
                //Changes were applied successfully.
                //doing some DOM stuff and notifying the client

                //check again after 5 seconds
                setTimeout(function(){
                    check_file();
                }, 5000);
            }
        }
    });
}

Server side (action_1.php):

//update database
echo '{success: true}';

Second way:

Client side:

function action_2()
{
    $.ajax({
        url:'http://www.example.com/action_2.php',
        success: function(data)
        {
            var result = $.parseJSON(data);
            if (result.success)
            {
                //Changes were applied successfully
                //doing some DOM stuff and notifying the client
            }

            setTimeout(function(){
                action_2();
            }, 5000);
        }
    });
}

Server side (action_2.php):

if (file_exists('somefile.txt'))
{
    //update database
    echo '{success: true}';
}
else
{
    echo '{success: false}';
}

In the first way, I am calling the server twice (Request/Response/Request, please note first request is only requesting for the HEAD), and it is using Apache's default scenario to check the file availability (that I don’t know how it is working).

But in the second way, I am calling the server once, and it is using the PHP file_exists() that it mean it need to load PHP environment first, then execute action_2.php.

Because the file is not mostly existent and because it need to handle maybe millions of requests, Then can you please guide me which way is better and why?