I have to vote LOTR purely for literary significance, and it's the benchmark against which all other medieval fantasy is measured against.
The Song of Ice and Fire is amazing in it's own ways.
English
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Do you think that the ASOIF series could have literary significance? It's probably hard to tell now because it's not even complete yet.
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Yes, but the heavy adult content will keep it from being assigned reading in middle school. I think Martin excels at character portrayal, I caught myself rooting for Cersei a few times when in truth I hated her. This is something I never had happen to me with the LOTR, though LOTR has such an authentic feel, and the poetry and songs in the books are incredible.