Targeting Parent Category Pages

You can do this using custom template and template_include filter.
category-parent.php and category-sub.php both are not required. One can be category.php for parent categories and for child categories, you can use custom-category-child.php as category-sub.php is reserved for default hierarchy.

• First create a template file in theme custom-category-child.php
• Then add this code to your theme functions.php

Update: As Pieter suggested we can use category_template instead of template_include to save few lines. Additionally we should return current template when our custom template file is missing!

Read inline comments

add_filter('category_template', 'custom_cat_templates');
/**
 * Create custom template for child categroies
 * @param type $template
 * @return type
 */
function custom_cat_templates($template) {
    $category = get_category(get_queried_object_id()); //Get the ID for current queried category
    if ( $category->category_parent > 0 ) { //Check if it child category
        $sub_category_template = locate_template('custom-category-child.php'); //return our custom template
        $template = !empty($sub_category_template) ? $sub_category_template : $template; //return default template if custom templaet missing
    }

    return $template;
}