Well, for me it is one of the worst in the DT catalogue, so no way it can be considered one of the greatest of all time..
But, leaving aside each one's personal taste, I think to answer your question one should ask wether this album is going to "change the course of music history" (= greatest).
And I think the answer to this question is a clear NO: no matter how much you like the songs or the production, or how amazing is the delivery by each band member, there are no musical breakthroughs in here, and it's certainly not going to create a new stream of progressive metal music, it is not going to push legions of teenagers to embrace an instrument, or anything like that.
The only DT album that can compete in this category is Images and Words: you might not love it as much as this one, but it certainly created (or at least reinvented and made popular) a musical genre (the progressive metal), even though a niche one.
PS - of course all of the above is just my opinion, it's not an universal truth, but I think it's going to be EXTREMELY unlike that this album is going to be more influential of I&W.
I think this is all fair. Counter argument is something like, Mozart's 40th symphony. Probably considered one of the "greatest", but as far as I can tell it was not more "influential". I'm not a classical music scholar so I could be wrong on that but I think it's true
This is a fair point...this debate could be never ending, as there's clearly not a mathematical rule to determine the "greatness"! 
By the way, also the 40th received "mixed reviews" !
https://it.wikipedia.org/wiki/Sinfonia_n._40_(Mozart)
According to Glenn Gould, it's 8 bars of genius in the middle of 30 minutes of banality!
(I could not find this quote in the English wiki).
Same thing as concerns Beethoven, the 9th, for example: it's certainly one of the most influential and popular, if not the most, but I would not consider it one of his masterpieces...
AVFTTOTW according to me does not fall in any possible definition of "greatest", anyway!
I&W IS the one! 
I mean...it changed the course of music history. It was different from anything anyone had heard up until that point in 2,000 years of Western music and not long after, it was in the mind of virtually every significant composer in the West after Beethoven. After the 9th and last, composers started to think of symphonies as pieces that their reputations would be built on. The genre would never be the same afterwards. By comparison, when Mozart began writing symphonies they were considered good concert openers. So, given the undisputed and virtually unparalleled historical significance, it's sort of asinine-- if not besides the point-- to say you don't consider it one of his masterpiece's. It's like my saying I don't consider the Sistine Chapel to be one of Michaelangelo's masterpieces (and might even be more egregious than my saying that). The course of history says otherwise. Your personal amateur opinion contradicting one of the great masterpieces of not only Beethoven, but Western art as a whole is sorta silly if not void of meaning.
Perhaps you just meant you prefer listening to some of his other works more than the 9th?
Well, the debate on the 9th is bit more complex than that.
A few years ago, for example, a famous Italian writer (Alessandro Baricco) wrote a book and directed a movie centered around a fictional character, Professor Mondrian Kilroy, that created a list of the 141 most overrated pieces of art in history. That list includes Metropolis (the movie!
) , 2001 Space Odissey, Moby Dick and others...
His "Lesson 21" (and the related movie) is dedicated to the 9th.
https://it.wikipedia.org/wiki/Lezione_ventunoApart from the obvious "fictional provocation" of the list, Baricco's point is that the "Western Cultural elite" has historically tended to magnify "complexity" over "emotions" in arts (I am over simplifying).
This book/ movie sparked an interesting debate, at least for nerds like me.
In other books he investigates how this "cultural model" has been attacked by Internet and the "quick consumption" culture ("the barbarians", how he calls them, even though not with a negative intent)
Going back to Beethoven, his point is that "genius" is often found in simplicity, not in complexity..and for example in the movie he "claims" (in a very romantic scene, by the way), that The Late Quartets (for example) show a much "higher content" of Ludwig's sheer genius, because it's not filtered by all the "cerebral complexity" of the 9th.
Some Sonatas also go much more directly to the heart of the listener...while you have to be "educated" to fully appreciate the 9th.
Where is the "genius"?
Well, I personally hear it more clearly in the Pathetique rather than in the 9th...but I am probably just one of the "barbarians", I am certainly not part of the Elite that "defines" what a Masterpiece is.
I think a similar story is true for DT...I fell in love with Images and Words because some songs there were just great songs that touched my heart, and only after I realized they were also "musically complex"...
In AVFTTOTW, for example, I was not stuck in the same way...you have to start from the complexity to "understand" the music ("don't you get that the Alien is in 5+5+7/16? that's genius!"), but that's not the path I like to follow when I listen to music.
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