I totally agree that when you aren't aware of much of Greyhawk's history, it is a hard setting to nail down what it's theme actually is.
I think when you imagine each campaign setting, it's always a good idea to reference a different, more popular fantasy property (whether or not it is released after or before) as a reference point. Dragonlance is an epic fantasy tale of a major war (or series of wars), much like Lord of the Rings or the Wheel of Time. Forgotten Realms is a cosmopolitan fantasy world with some clearly differentiated forces of good and evil (MMO World of Warcraft, or Ivalice Final Fantasy). Dark Sun is a post apocalyptic fantasy wasteland, where city-states compete for resources across a desert (John Carter of Mars).
Greyhawk most reminds me of two properties, at least in style: Moorcock's novels, and Conan the Barbarian. I'm going to use Conan as the reference as I have a better memory of that property and can better explain the similarities.
Conan of Cimmeria is an odd hero... in that he's barely a hero. He travels from adventure to adventure, fighting monsters and evil wizards, but his motivations are less than noble. Usually, he is fighting simply for survival, to take control of a kingdom, or just treasure. He behaves much like the PCs that Gygax and his original players made, who weren't particularly good-aligned, and instead were delving in dungeons for treasure, not to save a princess.
Our hero is the hero not because he's good, but because his enemies are worse. Much like Greyhawk, this is a world that requires an uncompromising and hard hero who is willing to stand up to the slavers of the Sea Princes, or the Hordes of Iuz.
The world of Hyperborea also matches Greyhawk in that it is a world in decline. Atlantis has fallen under the sea, and this is a new age with less of the previous splendor.
The common peasant will see little if any magic in their life, and treats it as a sign of demons. A smart move, since most practitioners of magic are indeed evil.
Of course, Conan is far more of a Bronze Age story than Greyhawk, which is more European medieval inspired. But tonally, I find Conan matches extremely well.
That's my explanation at least, I'm curious if people feel if I'm completely off my rocks.