Here's the case for LotR: Tolkien created an entirely new world, whereas Riordan did a bad job of meshing two preexisting worlds.. Many things that happen in Percy Jackson with real-world involvement simply wouldn't happen, and there are too many inaccuracies to Greek mythology for it to be glorified for that. On the other side, Tolkien's new world is realistic, relatable, and believable, while still being foreign enough to maintain a sense of mystique and wonder.
lotr*
I.must say, I enjoyed reading Percy J more than lotr, but lotr has more interesting lore, you could say.