Yes, this really is better than Lord of the Rings, better than the Ice and Fire series, better than anything else I've ever read.
The story takes place on the peninsula of the Palm, which is loosely based on mediaeval Italy. My knowledge of Italian history is little enough that I wouldn't like to comment on exactly how this has informed Kay's work, but the factual background here seems less intrusive than for A Song for Arbonne or Sailing to Sarantium; this is a fantasy world informed by history, rather than the other way round.
The peninsula was invaded by two wizards, Alberico and Brandin, who have captured four of the nine provinces each. As the last to fall to Brandin, the province of Tigana, did so, the wizard's son was killed in battle. As revenge for killing the son he loved above all else, Brandin obliterates all memory of Tigana, so that no one born outside the province can even hear its name.
Alessan, the only surviving son of the last Prince of Tigana, has sworn to avenge this, and claim back the name of his land. But to kill Brandin is not enough; as he recognises, only the the other's power holds both Brandin and Alberico in check. To be truly free, he must make the wizards destroy each other.
And I could summarise the entire book, and still not come close to why this story is so beautiful. I could talk about the use of fairy tale and legend: how Alessan, the youngest of three sons, is almost bound to be the one who completes his quest; of the twisting of an obscure line of Old Norse poetry into a great battle of good against evil; of Donar, the crippled blacksmith, and of the legend of the Golden Bough replayed: and how its foundation in scholarship makes Kay's writing so much richer. And it would still not be enough.
For me, the realisation of exactly how good this book is came from Brandin. The evil that he did is the very reason for the book's existence. Yet how much would you have to love your son to obliterate an entire people and their memory in his name? How much, to renounce your own hereditary kingdom and remain, watching the Tiganese die off, year by year, in the place where your love had died? How much, to know that in the end, only your own memory would hold the truth of what you had done, and why you had done it? How much evil can we do, over and over, in the name of love?
The point is, of course, that this world, its tragedy, triumph and high farce, is built around humanity. Kay does not need to create evil races, or on-going wars (JRRT, so help me, I am thinking of your orcs and the elves against the dwarves!) to make his magic. I think of Sandre, the exiled Duke, forced to choose between binding himself to his own magic and thus saving the life of his son but almost certainly being killed, or allowing his son to die and continuing to fight for his Dukedom's freedom. And Dianora, going to Brandin's court to kill him, but falling in love, asked to bind him and herself to his vision of what the Palm might become. And Rhun, the poor, broken Fool, given, at the end, a moment of honour. Gods help me, I'm crying as I write this.
And also the poetry of Kay's writing. "Tigana, may my memory of you be like a blade in my soul". And "You are the harbour of my soul's journeying". But also Catriona's ascerbity, the terrible words between Alessan and his mother, and Rovigio's good-natured insulting of his daughters, with the love he bears them never needing to be stated because it's so obvious anyway. Not one word too many, nor one too few.
And finally, the ending. Many people who like this book hate the end, in general accusing it of being too sudden. I will grant that the pace of the book increases manyfold towards the end, but this is natural. The Tiganese, Brandin and Alberico are in one place, having a battle; this is not the time to introduce a sub-plot! I grant, also, that while we do know the fates of around half the major characters, those of the rest are deliberately ambiguous. I can see that the extra ambiguity (or is it a clue?) of the very last line might be annoying, but it also leaves the reader free to imagine. This is an ending made by a storyteller, not an historian, because people go on, even when the stories that have brought them together are ended. Enough ends are tied to end the story, but without creating a great sealed knot.
It is simply the richness of the weaving that makes this so good, and no review can reproduce that. Please, if you only buy one book this lifetime, get this one.