I love both, but:
LOTR >>>>>>>>>>>>>>>>>>>>>>>>> HP
Both books and movies. LOTR is a literary masterpiece. It was written to challenge, engage, entertain and evoke emotion. HP, while extremely enjoyable (trust me, I love it), is just that.
When it comes to the films, LOTR was groundbreaking in every respect. Take ROTK, for example, becoming the first fantasy film to win an Academy Award for Best Picture. The screenplay was as true to the books as the writers could fit into a 2-3hr film. The HP films started brilliantly, but as an avid reader, they have now drifted too far away from the storylines in the books. As amazing as the action is, much of Rowling's original story has been lost because of it.
I'd like to reiterate, I love both - books and films. But nothing is better than LOTR. Nothing.