I have immensely enjoyed both series, but LOTR really wins without any question for me.
I love the detail that Tolkein put into creating not just a story, but a living world, one that keeps on going - and he enthused the entire of Middle-earth with a history almost as vibrant as our own.
And the languages... Elvish, Dwarvish, Black Speech, and more.
Each culture is distinct - and while tied to some real-world cultures, it's not obvious - sure the Dwarves are like Vikings, and Rohan similar to the Saxons, but you don't realise it.
I do like Harry Potter, but never as much as I could like LOTR.