get post by nav id

I think you need to loop the $menu_items because the function, according to the Codex, returns a array.

Remplace echo $menu_items->ID; with

 foreach ( $menu_items as $menu_item ) {
    echo $menu_item->ID;
 }

I need to check the array exactly, but if you need to compare a post ID to a menu item, you will need to compare $menu_item->object_id which contains the ID of the post the menu-item is linking to.