Is it better to use module_invoke_all(), or  module_invoke() and module_implements()?
There is little difference; module_invoke_all() runs the following code:

function module_invoke_all() {
  $args = func_get_args();
  $hook = $args[0];
  unset($args[0]);
  $return = array();
  foreach (module_implements($hook) as $module) {
    $function = $module . '_' . $hook;
    if (function_exists($function)) {
      $result = call_user_func_array($function, $args);
      if (isset($result) &amp;&amp; is_array($result)) {
        $return = array_merge_recursive($return, $result);
      }
      elseif (isset($result)) {
        $return[] = $result;
      }
    }
  }

  return $return;
}


The only difference is that with module_invoke_all(), for example, func_get_args() is invoked only once, while when using module_invoke() func_get_args() is called each time module_invoke() is called; that is a marginal difference, though.
There are a few cases where module_implementing() and module_invoke() are used, normally when a module needs to know which module is invoked, such as in the case of search_get_info() that builds an array of information about the modules implementing search functions.

function search_get_info($all = FALSE) {
  $search_hooks = &amp;drupal_static(__FUNCTION__);

  if (!isset($search_hooks)) {
    foreach (module_implements('search_info') as $module) {
      $search_hooks[$module] = call_user_func($module . '_search_info');
      // Use module name as the default value.
      $search_hooks[$module] += array(
        'title' =&gt; $module,
        'path' =&gt; $module,
      );
      // Include the module name itself in the array.
      $search_hooks[$module]['module'] = $module;
    }
  }

  if ($all) {
    return $search_hooks;
  }

  $active = variable_get('search_active_modules', array('node', 'user'));
  return array_intersect_key($search_hooks, array_flip($active));
}


Another example is image_styles(), which gets the list of all the image styles implemented by the modules, and that uses the following code:

  foreach (module_implements('image_default_styles') as $module) {
    $module_styles = module_invoke($module, 'image_default_styles');
    foreach ($module_styles as $style_name =&gt; $style) {
      $style['name'] = $style_name;
      $style['module'] = $module;
      $style['storage'] = IMAGE_STORAGE_DEFAULT;
      foreach ($style['effects'] as $key =&gt; $effect) {
        $definition = image_effect_definition_load($effect['name']);
        $effect = array_merge($definition, $effect);
        $style['effects'][$key] = $effect;
      }
      $styles[$style_name] = $style;
    }
  }


In both the cases, the retrieved information is put in an array where the index is the short name of the module.