Which one is grammatically correct: "one of the great" or "one of the greatest"?

I have been playing a typing game for a while now. The text starts with:

Aesop was one of the great Greek writers...

Is "one of the great" grammatically correct?

Solution 1:

Aesop was one of the great Greek writers...

and

Aesop was one of the greatest Greek writers...

Are both grammatically correct and mean the same.