The thing is, the reason JWs don't watch magical things isn't just because: "magic bad".
There's a reason behind this. That is spiritism. Now, the only way to practice magic, in reality, is to have help from demons. That is detrimental to a servant of Jehovah. Watching media portraying people contacting demons is also bad.
However, the magic in Lord of the Rings is quite different. The Ainur are the source of all magic. Some Valar and Maiar are evil, and become demonic figures, whilst some are good, and remain angelic figures. The magic in Lord of the Rings, therefore, comes from either angels or demons. The magic used by the good guys always comes from the angels, and therefore cannot be equated to magic nowadays that can only come from demons. Therefore, watching Gandalf heal Theoden is not spiritism. But, the magic that Sauron and his forces use does come from demons. So, the Ring is a demonic possession, and so watching Frodo put it on is a form of spiritism. This becomes a dilemma - do you watch or read something containing explicit spiritism? Well, to some, this spiritism is clearly condemned in both the books and the films, and in the end, it is destroyed. Moreover, the magic used doesn't resemble the magic being practiced today and is a secondary element to the story (the Ring's power to corrupt people is a more prominent feature than the fact it is magical). To others, it contains spiritism and therefore they cannot watch it. The fact that the magic is more subtle is likely the reason that more JWs are fine with it.
Harry Potter is different. The magic comes from the individual based on whether they inherit it or not. Compared to reality, this is fantasy, and the magic being used clearly has a resemblance to magic being practiced today (wands, spells, etc.). So, more JWs are likely to not be fine with it because it may remind them of actual spiritistic magic, even though the magic being practiced isn't technically spiritistic. To others, since the magic is not spiritistic, it is just fantasy and is ok to use.