Comparing LotR to ASoIF feels like comparing the old testament with the new or something.
Personally, I get a bit too nostalgic about LotR and all the stuff that's come with it (music, art - especially before the movies) to not choose that one. But ASoIF has better character development and I really love all the political intrigue.
I'd like Harry Potter more if the author wasn't who she is... in all fairness though, she's good at writing books and should stick to that instead of speaking about politics and stuff. Can get a bit nostalgic about HP (the sauce is damn good too lol) as well, I mean - who wouldn't want to be a Slytherin?
But its nowhere near the others. A better comparison would be Discworld or something, maybe Dune. As for favourite fantasy setting its Glorantha (think you should like that one too Hrafn...) which is actually originally began as an experiment by a practising real life shaman a way to deepen his own understanding of mythology. Apart from the King of Dragon's Pass game though... and some fan stories, there's unfortunately no Magnum opus for that one. Yet.