There's no objective "better", despite what you'll hear from music fans.
LotR, while I've never read it, has pretty comprehensively established itself as a deep, staggeringly well-written epic that invented modern fantasy. That's incredible. Its drawback is that it's damn near impenetrable and moves like a snail. If you're intelligent and have a long attention span--which doesn't make you better than people lacking those traits, by the way--it's a better read for you.
HP is more modern, but eventually both series will be outdated, so let's ignore that part. The writing isn't as good, but the HP universe is comprehensive, doesn't require a college course to understand, and knows exactly what it is: a festival of tropes. It keeps you reading, and even though the books are doorstoppers, stuff's happening and it moves like a piece of potassium rocketing across a pond, complete with sparks and I forget where this simile is going. If you're less of an intellectual and want an easier read, HP > LotR.
It comes down to what you want in a book, honestly. They're both extremely popular and have left their marks on the world of literature.
