Category Template to Show Different Elements for Child Categories

I’m looking at this idea for my category (archive.php) template:

– if it is a child category page
Show post titles only

– if it is a parent category page
Show the regular title photo, excerpt, etc.

<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>

		<!-- parent/child template -->
		<?php
			$cat_obj = $wp_query->get_queried_object();
			if( $cat_obj->parent ) :
		?>
			<!-- child category -->
			<h4><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a> <?php edit_post_link(__('<span class="edit_link">Edit</span>')); ?></h4>

		<?php else : ?>

			<!-- parent category -->
			<h2><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a> <?php edit_post_link(__('<span class="edit_link">Edit</span>')); ?></h2>

etc.

It totally works fine. But I want to show 10 posts for the child category instead of the default. The default would still show for the parent.

This seemed like an easy task until I started trying to figure it out. Can anyone help, please? I’d be happy to trade for any design/css tip you may need.