After creating the Comment History page, I realized the Recent Comments Plugin was listing the comments in order from newer-to-older, instead of older-to-newer (which is how the comments on my post pages were ordered). I thought that I should probably change the ordering of the comments on my post pages to match the Comment History ordering.
The solution, I discovered, was rather simple. Just open the comments.php file in your theme's home directory, find this line:
<?php foreach ($comments as $comment) : ?>
and immediately above it add this:
<?php $comments = array_reverse($comments, true); ?>
Save the file and your comments will be ordered from newer-to-older. However, after making the change I realized my original older-to-newer ordering made more sense. Why? Because when someone is reading a post, the first comment they read might not make any sense unless they have read a previous comment.
So to make reading the post page more user-friendly, comments should be ordered from older-to-newer (the WordPress default). For a Comment History page however, ordering comments from newer-to-older makes more sense because the visitor is probably viewing the Comment History page to check for the most recent comments on a post they have been following.