Wordpress - how do I know if a menu item has children?

It seems that the problem has finally been addressed. The latest Wordpress beta as of current writing 4.0, has updated the Walker_Nav_Menu class and added a $has_children property.

/**
 * Whether the current element has children or not.
 *
 * To be used in start_el().
 *
 * @since 4.0.0
 * @access protected
 * @var bool
 */
protected $has_children;

So, we don't need to hack function display_element(...) anymore.

Add this to functions.php it will add the 'dropdown' class to parents

New way beter for performance

function menu_set_dropdown( $sorted_menu_items, $args ) {
    $last_top = 0;
    foreach ( $sorted_menu_items as $key => $obj ) {
        // it is a top lv item?
        if ( 0 == $obj->menu_item_parent ) {
            // set the key of the parent
            $last_top = $key;
        } else {
            $sorted_menu_items[$last_top]->classes['dropdown'] = 'dropdown';
        }
    }
    return $sorted_menu_items;
}
add_filter( 'wp_nav_menu_objects', 'menu_set_dropdown', 10, 2 );

Old: intensive on the DB

add_filter( 'nav_menu_css_class', 'check_for_submenu', 10, 2);
function check_for_submenu($classes, $item) {
    global $wpdb;
    $has_children = $wpdb->get_var("SELECT COUNT(meta_id) FROM wp_postmeta WHERE meta_key='_menu_item_menu_item_parent' AND meta_value='".$item->ID."'");
    if ($has_children > 0) array_push($classes,'dropdown'); // add the class dropdown to the current list
    return $classes;
}

Simple you use this way:

Explain: I create menu with "walker":

$walker = new Nav_Walker;
wp_nav_menu(array(
        'container'=>'nav',
        'container_class'=>'menu',
        'menu_class'=>'list-unstyled list-inline',
        'walker'=>$walker
    ));

Class Walker:

class Nav_Walker extends Walker_Nav_Menu
{ 
      public function start_el(&$output, $item, $depth = 0, $args = array(), $id = 0)
    {
        if($args->walker->has_children)
        {
            //code...
        }   
    }
}

We have object 'walker', you can var_dump($args) to see more things. I'm using for my project !