I came across the following sentence in an English book:
One of the great unsolved murder mysteries of all time is that of "Jack the Ripper".
What difference would it make if the word great is replaced with the superlative form, greatest?
I'm going to use baseball players in my answer, because I don't feel like writing an answer that seems like it is grading the greatness of murder mysteries ("Zodiac Killer, I give that mystery a B-, but Jack the Ripper was an A+ mystery"). That example also shows how there can be a difference depending on whether you are talking about a person, because of the "greatest of all time" idiom.
"Great" means "considerably above the normal or average".
A "superlative" is a word indicating something "of the highest quality or degree".
So already you can see that great vs greatest can be, in some context, saying kind of the same thing, about where something goes in a hierarchy; although superlative is even more about being near the top of some hierarchy.
And of course, the phrasings are both about saying what group someone is "one of": (1) "one of the great baseball players" or (2) "one of the greatest baseball players." So the question becomes whether those groups are the same or different.
They mean pretty much the same thing. Saying those both myself now, if I heard them in a casual conversation by themselves and wasn't thinking hard about it, I think they bring to mind the same set of people. I would not think the speaker had a significantly different analysis or intention if they said one or the other, if we were just sitting around chatting about baseball.
Sounds Kind of Like G.O.A.T. However, once you add "of all time" there's the idiom "greatest ________ of all time". So saying "one of the great ______ of all time", while not wrong, sounds mildly weird because you've almost but not quite said the idiom, which seems like the easier and more familiar way to say it.
Just doing a Google quoted-search right now for "one of the great", it's usually part of a more qualified or nuanced assessment. For example, "one of the great _____ of the 20th century" is a pretty common usage. "One of the great _____" also sounds less weird with abstract things rather than people, so like your author writing about murder mysteries.
Greatest is slightly more elite. If I did think hard about them, I would probably think that "one of the great baseball players of all time" would be, like, the top 100. And maybe "one of the greatest baseball players of all time" would be a smaller group, maybe the top 10. But those are very arbitrary and fuzzy boundaries that imply a kind of precision that most people don't use in ordinary conversation, and different people would think of different group sizes.
It's sort of like the difference between saying "one of a small group" and "one of a very small group". Both "one of the greatest" and "one of a very small group" seem more elite or limited, but then who knows exactly how small of a group we were talking about here in the first place, because it's not a quantitative analysis.