Greyhawk, in my opinion, needs to have its own identity so that it can stand out as a distinctive world from the Forgotten Realms or Mystara. It used to be thought of as the world of classic dungeons, but with Tales of the Yawning Portal, those dungeons can appear in any world.
My knowledge of Mystara is pretty limited, but it has always struck me as more monarchy/nobility focused than GH or the FR. I do think GH's identity, while somewhat muddled over the decades, still separates itself significantly from FR. While both include many of the same fantasy tropes (magic, elves, dwarves, gods, etc.), Greyhawk has a more bleak geographical and political landscape than FR. Good and evil have battered each other to a standstill, evil with the slight upper hand. So the world has a more dark, oppressive tone compared to FR's brighter, good-shall-prevail outlook. Of course, FR has its share of gloominess, just as GH has its beacons of hope and light, but the overall grim atmosphere of Greyhawk is what distinguishes it from FR.
Greyhawk as a published setting is an artifact of its time. The kind of fantasy it represents is a mid-70s aesthetic. Some folks like to say that the difference between Greyhawk and FR is that Greyhawk is "sword and sorcery" while FR is "high fantasy", but I think that's not quite right. Greyhawk has its share of Tolkien tropes and FR has its share of Howard inspired sword and sorcery tropes and you can do either high fantasy or sword and sorcery in either setting. It's more that Greyhawk as published is a very 1970s vision of fantasy, while the Realms as published are a very 1990s vision of fantasy (except for the grey box, which is a very 1980s vision of fantasy). Where Gygax threw together a world based on Howard and Lieber and Tolkein and Moorcock and other authors who published in the span from the 20s through the 70s, the authors who grew the Realms from Greenwood's original vision were all influenced not just by the authors that influenced Gygax, but also MANY other authors because the 60s/70s/80s were an explosion for fantasy. Authors like Eddings and Brooks and McCaffrey and LeGuin and later even Weis and Hickman and their Dragonlance books all influenced the people who grew the Realms from Greenwood's original vision, making it a more contemporary fantasy setting while Greyhawk sat untouched by the publishing schedule for the most part and didn't grow in that way.
I agree with most of this, but I don't think that's to Greyhawk's detriment. Its pulp fantasy-era roots define it as a setting and it isn't any more dated than reading Howard or Leiber or Moorcock today, and certainly no more (or less) dated than an 80s/90s vision of the FR. Both have very different but equally valid approaches on the fantasy genre.
It's been in the hands of players for a far longer span of time than it was actively being published by TSR/Wizards. And all of those players have their own vision of what Greyhawk is. The Realms had dedicated line editors and authors (like Greenwood and Salvatore) to define what the Realms were for players from the time it was first published until fairly recently (and still has Ed Greenwood somewhat acting as the Voice of God). Greyhawk was left without anyone in TSR/Wizards to set direction for it and so players were on their own. And each of them developed their own vision of what was important in the setting and what was to be ignored.
Only once 4th edition was released in 2008, but until that point Greyhawk was still very much a prominent presence to WotC and TSR before them. Sargent, Cook, and Moore all guided Greyhawk into the 3rd Edition era, where writers like Holian, Mona and Jacobs then carried the torch. That's a pretty respectable roster. Sure, some of the changes these authors brought created strife among GH fans, just as changes like the Spellplague was divisive for FR fans. Changes to the campaign setting are as inevitable as the schisms it creates, but that isn't something wholly exclusive to Greyhawk.
