I don't think this is an either or question. There's a spectrum between focused and general were most campaigns fall.
For my part, most campaigns I've played in are more focused than what you call general and more general than what you call focused.
For example: "You're going to start in this city. Here's a page or so of fluff for it and the surrounding area. The format of the campaign will be fairly wide open sandbox. I've got pretty detailed fluff for this world so you can go pretty much anywhere you want, no need to stay in the city if you don't feel like it, though there's plenty of adventure hooks there if you want. If you're looking for something to get you started there's this organization called the Adventurer's Guild and they are known to form teams and give out missions to them. Be aware that this is a pre existing world, not something I'm making up tailored to you guys. Not every encounter you run into will be level appropriate so know when "run away!" is the correct strategy."
That's just one example. Different games fall in different places and both ends of the spectrum (as well as the middle) can be fun if well executed.
Would you run a campaign where most of the enemies were undead or where a large portion of the action took place at sea and not mention that to the players beforehand? I would find that a bit odd, not only because you risk screwing over a player but because the players lose out on using various environment specific options that can be fun but are far too situational to take in most campaigns. I mean, I could definitely see the appeal to playing a Dire Shark riding Merfolk, but I'd never build that character unless I knew it was going to be an aquatic campaign (for obvious reasons.)
Also, in not cluing the players in, you actually swing the balance bar yet further towards casters and away from everyone else. Prepared casters, at least, have a pretty easy time switching things around to account for idiosyncratic settings. Wizards need to find a magic mart and Clerics/ Druids can just dig through books and switch around their memorizations. For most other characters you pretty much have to wait to level up and even that won't help you all that much depending on your situation. This is a pretty minor point but my preference is to avoid giving casters more advantages than they already have.
EDIT: Rereading your post, this passage seems really strange to me:
The General Campaign. This is where the DM makes up a setting and each play makes up a character. The DM only reveals tiny bits of information needed for character creation, like ''you can't be an elf''. Each player is free to make any type of character they would like with in the house rules. The players have no idea about the setting (''it is just like Earth'') and they have no idea how the campaign will go(''anything can happen".
The bolded portion doesn't make sense to me. Are the characters all amnesiacs? If not, then they would have a pretty clear idea about the setting, at least to the point of knowing about the village/town/city they were born in and probably a little about the nation/city state/empire/feudal fiefdom it is a part of and the god/gods/lack of same that are worshipped there. And that's a bare minimum. If a player invested in Knowledge (Local) (or history or geography or nobility and royalty or religion or the planes) they'd know more and if the campaign started above level 3 or so and the characters had travelled, they'd know a lot more.
I don't expect an atlas, farmers almanac, and holy bible written specially for every campaign I play in but "the players have no idea about the setting" throws me for a loop. If I had no idea about the setting, how would I write my backstory? I'd end up inventing a setting as I was going along and if all the players did that (without consulting with each other) you'd likely end up with a missmatched mess.
