I think one of the biggest differences in the LoTR books versus the Harry Potter books is that the LoTR books are more detailed oriented which presents a slower progression and is less likely to be enjoyed by people less than 30 years old that grew up on fast paced video games, movies, television shows (and 200+ channels), etc. being the "norm" for them.
People older than 30 appreciate the attention to details and tend to be more patient with parallel events/scenes in books where younger readers tend to want linear stories that move along at a decent (not too fast, nor too slow) pace. Younger readers also want books that focus more on the important details and less on the not-so-important details.
Another variable in this is that most older people read LoTR before ever seeing the movies because they read the books long ago. Most Harry Potter fans saw at least one or two movies before reading the books. This means that to them, the locations, scenes and characters were already established for them from the movies. Most fans of the LoTR books read the books first so they saw the books come to life in a sense creating a grander and more appealing appreciation.
This by the way is not meant as a criticism of either style of reader .. it simply explains the preferences of people tend to follow age groups and/or how they were introduced to each of the fantasy stories.
Personally, I like the books of Lord of the Rings and Harry Potter a lot more than the movies of either. I think that both sets of movies succeed at reproducing their respective fantasy worlds but the pace of the movies tend to rush the stories along and fail to provide a true feeling for the amount of time that passes between events. In fact, most people are absolutely stunned when you inform them how much time passes between events in LoTR.
-Reality