The Lord of the Rings franchise is definitely larger and older than the Harry Potter franchise. The first Lord of the Rings books came out inthe late 1970's whereas the first Harry Potter books came out in the late 1990's. The Lord of the Rings therefore, has had an additional 20 years to gain a following and build a franchise including books, movies, video games and merchandise.
New Zealand even used a Lord of the Rings airplane to promote the series. When you compare box office sales however, Harry Potter films made $7.7 billion for 8 films, whereas Lord of the Rings made $2.9 billion for 3 films.