Using system date format

Calling get_the_date( get_option('date_format') ); will return the exact same value as get_the_date(); this is because by default if a date format is not specified when the function is called it will use get_option('date_format'); as can be seen from the following snippet taken from the get_the_date() function itself:

if ( '' == $d ) {
    $the_date = mysql2date( get_option( 'date_format' ), $post->post_date );
} else {
    $the_date = mysql2date( $d, $post->post_date );
}