Are you referring to books and movies made from them in general? Or specifically to LoTR?

I generally read the books before seeing movies. Often this is just because I've read the novel long before the movie ever got made. And I've found that I prefer doing it in that order, because the novels will usually have a lot of subtle context and details that they simply don't attempt to capture on film, because it would be too much to try to put it all in the movie. And sometimes they'll change the ending in the movies (sometimes this is for the better, other times, it's for the worse).

However, if the novel is a tie-in, written specifically to accompany the movie, I will usually see the movie first to avoid spoiling the movie. In most cases I thought this worked well. I wouldn't have wanted to spoil Star Trek II: The Wrath of Khan -- but I did find that the novelization had way more detail and context which really enhanced the movie in hindsight.

As far as LoTR, I have to admit that I read it many years ago, long before the Peter Jackson movies, and honestly, it was enjoyable enough for me to read it once, but no more than that -- but I am just not the world's biggest Tolkien fan. I enjoyed the movies simply because -- perhaps especially because -- they did not try to cram in everything from the books.