I disagree that LOTR has "very important and strong women" in it. Both Galadriel and Arwen are marginal characters, IMO, in the same way that women are marginal characters in the Odyssey. Women aren't often central characters in any epic myths, because epic myths are, for the most part, male adventure tales.

I'd also like to add that both Harry Potter and LOTR lack one essential ingredient to good storytelling: sex.