I'm really struggling to think of any other fantasy epic that even came close. Tolkien's writing and grasp of the English language was superlative, whilst most of his imitators were not only derivative but also somewhat lacking in actually writing ability and flair.
Not epic in the same way, but I think Michael Moorcock took a lot of what Tolkein and previous fantasy authors did and turned it on its head.
It was no longer good vs evil, but law vs chaos, and both sides were capable of good and evil, but mainly they were amoral. The "Elves" were not some sort of wise beings living in harmony with nature, they were decadent, cruel, sadistic, chaos worshippers. The heroes were generally not buff barbarians but in the case of Elric, a weakling wizard prince who only can live through the use of certain herbs, sorcery, or by sucking the souls of people through his sword.
What Tolkien did for mainstream fantasy Moorcock did for what might be termed alternate fantasy.
I'm not saying Moorcock was a great author. The man himself admits to being a hack and was pumping out books in the early days just to pay the bills.
Also Moorcock didn't just have an impact on fantasy, his motifs and icons can be found in music, other genres of books, and art.
He even had his own band (it wasn't that good though)
One of the bands he influenced was Hawkwind, who some might remember for their song Silver Machine or others.
They dedicated an album to his themes
Another lesser known band took their name from one of his themes as well, the Tygers of Pan Tang
Maybe you have heard of a band called Blue Oyster Cult (of Saturday Night Live cowbell sketch fame)?
As well as a number of other lesser known bands.

Chronicle of the Black Sword: Rock and Metal Inspired by Michael Moorcock’s Multiverse
Heroic fantasy has always been a popular lyrical subject for heavy metal bands, and it’s not hard to see why. Heavy metal simply isn’t normal. You just can’t write powerful, dynamic compositions an…

And in terms of art, Rodney Matthews' distinctive style was used for some of MM's publications, especially Elric at the End of Time
