I put both, which is always hard for me to admit. The scope of the book, the pure fantasy, the greatness of what it is and what it means to literature, as well as the fantasy/sci-fi genre is akin to the Declaration of Independence to the whole of American History.
If it's taken at face value both LotR and TDoI are merely written documents. The LotR are simply an ego stroke for Dr Tolkien if looked at objectively and TDoI is simply a nasty-gram to the government (something that is done daily via the interwebs.) But at the same time, they are pivotal in what comes after. Without LotR it is likely that what we know as Fantasy literature would be much different and without TDoI the scope of American government would also be different, not that they wouldn't exist, or that they may not even exist as we know the, but it is doubtful. (Enough about American History)
The style of writing Dr Tolkien used in LotR sometimes makes my head hurt. The story is great, but often times I wonder, why it was written the way it was written, and if submitted to a modern editor what the large volume of red marks might look like. (especially concerning timeline and pacing.) And honestly, if they could ride giant eagles out of Mordor, couldn't they have just ridden them in and dropped it down the volcano? (Medieval bombing run?)
But the story that transcends time, at least for me, is the characterization. The little lessons that were drawn from his experience in WWI: The horrors of trench warfare (the depiction of battle as grim and gruesome versus glorified); The dangers of industrialization without forethought (the trees of Isengard); The contributions that one small individual can make to the greater whole (all over the books); and that special relationship versus and unit officer and his top enlisted (Frodo and Sam (and no it isn't a metaphor for homosexuality as some have tried to state)). He literally took the horrors of his combat experience and turned them in a positive light, something modern mental health personnel are trying to get PTSD sufferers to do.
So for all it isn't, it is still a great piece of literature. So yeah, there are parts that just plain suck eggs, but it doesn't kill the overall effect of a(the) great book(s). But that's just my opinion.