I'm really not sure.
Dune has some stupid, stupid concepts and its treatment of sex and race has aged if anything worse than LotR's but the central conceits--the Spice and the sandworms--are fantastic.
Doctor Who is too disjointed, sprawling, and massively variable in quality to really count as a coherent universe. Heinlein's terrible and I'm not familiar enough with Asimov or Clarke.
Teito monogatari has some really cool intuitions about
setting but its sensibilities are even more reactionary than is usual for the sort of story that it is and I'm also not sure it counts as science fiction;
Legend of the Galactic Heroes has the former problem as well as some of
Dune's problems but not as severely. There's something mean-spirited that I detect in a lot of Douglas Adams's work but his concepts and style do hold up well. Something has started to piss me off about the Hainish Cycle--which I'm sadly unsurprised no one else has mentioned--and I can't quite put my finger on what it is. I guess I'd say that's still overall the best-conceived.
But my point is that overall LOTR is the choice for the best of the Fantasy genre that everyone usually agrees on (with Potter, EarthSea, Narnia, and ASOIAF close to it),
I like all those series to varying extents but I wouldn't describe any of them as approaching LotR.