How to override node comment form template?
In Drupal 7, and in the case of the user login form, your trick works because the form doesn't set the #theme property; in that case, Drupal will use the theme function whose machine name is equal to the form ID. (For the login for, that is user_login.)
That is not true for the comment form, for which its form build (comment_form()) sets the #theme property.

$form['#theme'] = array('comment_form__node_' . $node-&gt;type, 'comment_form');


There isn't a match between the machine name of the theme the form builder wants to use, and the comment-edit form ID; the latter is comment_node_CONTENT_TYPE_form, not comment_form__node_CONTENT_TYPE. If you were defining a comment_form theme function, that should work.

In Drupal 6, there is no #theme property for comment_form, which is the form ID of the comment edit form.