This article, from
The Christian Guide to Fantasy, talks about various literary devices used or not used in Narnia, Lord of the Rings, or Harry Potter, which create 'literary hedges' around the magic found in such series. The author raises concerns about the Potter series as compared to the others, which have more of these literary hedges.
http://www.christianfantasy.net/sdg1.html
An excerpt:
"But is there equally no risk of young Harry Potter fans developing an unhealthy infatuation with the idea of magic, and in particular with the idea of studying and learning magic? Might not such infatuation, at some later date, in the absence of adequate parental guidance, be one factor influencing a child to respond more positively or with greater tolerance toward everyday occult phenomena? Might it be one factor influencing a child to respond with greater interest or tolerance to Wicca, or the Kabbalah?
"These seem to me reasonable concerns; and Christian parents may want to be aware that Rowling, unlike Tolkien or Lewis, doesn't seem to share them. Consequently, greater parental guidance is required to avoid the pitfalls of the use of magic in the Harry Potter books than in The Lord of the Rings or The Chronicles of Narnia.
I don't mean to suggest that the absence of these literary safeguards in Rowling automatically makes her work inherently unacceptable, harmful, or even necessarily morally inferior (though I do in fact think on other grounds that it is somewhat morally inferior). But I think that Christian readers, and particularly Christian parents, should be aware, first, of the pitfalls that always attend the use of magic in literature; and second, that Rowling has not given them the safeguards present in Tolkien and Lewis; and that if their children do read the Harry Potter books they may need extra guidance to avoid these pitfalls, which would not be the case with respect to The Lord of the Rings or The Chronicles of Narnia."
An issue with your quote:
Narnia and Lord of the Rings have existed for a number of decades, whereas Harry Potter is recent. Also, Lord of the Rings has a very strong cult following, which is similar to Harry Potter -- Harry Potter having a stronger base due to the simpler writing and faster plot.
Also, LotR and Narnia have, almost entirely, black and white situations (LotR exception being Smeagol). Harry Potter, on the other hand, has a number of characters in situations which are clearly not black and white, and, in my opinion, show the importance of conscience development and factors which can go into their development.
Harry Potter, especially the last four books books, are NOT for children under the age of 14, in my opinion, simply due to the over-arching theme of the book's gravity (death and love). Also, in book five, there is a lot of teenage angst and hormones, which may be difficult for a pre-teen reader to understand. Narnia does not have all of these things (okay, death and love is in the first), and Lord of the Rings requires a higher reading level (8th grade or higher). My Aunt would read Harry Potter to my cousins, but would pre-read the chapters and leave out some of the more...sad?, difficult? passages out. If pre-teens read the earlier books, yes, they may get caught up in the fantasy, but once they reach adolescence, they will realize it is just that, fantasy.
Also, just to point out, the article does NOT state that parents cannot or should not allow their parents to read Harry Potter books, but rather that they should make it clear that it is fiction and that practicing magic (not illusions for entertainment) is sinful.