Depends what you want from a book. 'The Lord of the Rings' is mythic it addresses fundamental questions in a dreamlike narrative, with all the gristle removed. It's the Disney version. 'The Song of Ice and Fire' is steak with the hair on, it addresses big questions but revels in ambiguity, it's a worms-eye view. The Quentin Tarantino version.
There's way more going on in asoiaf and way easier to digest for me. And it's real interesting how it's perspective based and not story based. I liked the lord of the rings, but god knows there were a lot of moments where it just felt like wandering and moaning, kinda like the 7th Harry Potter book, but better
I just read "A Song of Ice and Fire" (book 1 and half of the second book) and I liked it a lot, I just stopped reading because of my studies that took me more time. I never read "The Lord of the Rings", so I can't really say.
I think they are too different to compare honestly But if i had to choose i would say overall GoT has a better story But seeing as lotr was writting 60ish years ago and only has 3 books but is still overall just as good as got I vote lotr Plus its like the father of all fantasy And if you include the hobbit thats one of my favorite books