Using get_cat_ID

I’m trying to develop a template that gives a listing of either category titles or post titles, depending on whether the link points to a category that is just a parent of other categories or to a category that has posts.

So far I have the following:

<h2 class="pagetitle">
  <?php single_cat_title(); ?>
</h2>
<div class="list-page">
 <ul>
  <?php wp_list_categories('orderby=name&child_of=4&title_li='); ?>
 </ul>

Obviously, this works fine for the one category in question, which has none of its own posts but a parent to other categories. I’m at a loss however for how I need to alter this for my desired result.

Thanks for any help.