I've just accidentally stumbled upon your question now-it's interesting-mind you the dearth of responses perhaps says something about reading and literature itself....
I don't know what book would be but I imagine there's a few in contention-the ones which you've already named and other obvious ones like Don Quixote,etc.
Whether it would tell us very much about the quality or even the influence of said book is debatable for many reasons-one being that once a book acquires classic status it tends to gain a life of it's own-attracts reverence and rarely gets critically evaluated by too many of us thereafter.Plato is a point in question-those who love/admire hang slavishly on every word as though they were as relevant today as then-they're not-but few feel entitled to say so -when Plato talks of his ' perfect society ',he has a few screws loose,sounds almost fascistic(yea I know the word fascist is wildly overused and often inaccurately and I do appreciate that Plato was important and well ahead of the pack for his time).On the omission of religious texts....I'm not sure that they should be excluded as the very fact that they are still read by a great many serious thinkers in such a scientific age bears testimony to how well put together they actually were even if one is not religious at all.

In the West it would be Aristotle, hands down.

Stock in Plato has wavered, and his influence was channeled into religion via Plotinus and the neo-Platonists, but Aristotle has been the foundation -- love him or hate him -- of the entire Western Canon.

And remember that even in the so-called Dark Ages, Aristotle was preserved and debated in Arabic. He's been the longest-running continuous show since the discovery of fire.

Homer wins if the discussion is strictly Western literature. Which it's not. But which is all I really know...

And if you forget when he wrote, and consider only the range of influence since he left the stage, then it would have to be Shakespeare. Is there actually a second place?