how to change order on comment form

i would like to have the comments input field first then the name / email etc after it.
I could shift it via jQuery –

function change_position() { 
?>
<script>
(function($){
	$('#wp-comment-wrap').insertBefore('.comment-form-author');
})(jQuery);
</script>
<?php
}
add_action('wp_footer', 'change_position');

but i guess an own comments.php would be the better solution. Is there an easy way to do it. Guess the form is set in comment-template.php of wordpress – but i like to have an update save child-theme solution.