I think they're all different kinds of sad. The Exigency is purely miserable. There's no comic value to it. It's saddening and disheartening and that's what it's supposed to be. I don't think there's been anything remotely resembling a joke on that blog, which is fine! Like I said, that's what it's supposed to be and it's doing a very good job at it.
John and Unskilled are more on the line of sad/funny, or to use the official word, tragicomedy. I'd argue Unskilled plays into tragicomedy more whereas John is so sad it's entirely hilarious, so for the sake of this little thing I'll use Unskilled as the example.
Half of what Unskilled says and does is a joke. And a lot of said jokes are very self deprecating and self referential. It's impossible to ignore. Then of course there's the copious amounts of dark humor, or to use Mewo's term, gallows humor, which is arguably more fitting in an ironic fashion, as the term originated from the kind of humor made by death row prisoners right before execution. The kind of humor on the blog really hammers home the fact that even when being lighthearted, the misery is always palpable. It's sad and disheartening, but in a way that makes you think This really shouldn't be as funny as it is. I'd argue it's made to be relatable. Most people don't express sadness like the Exigency, but in the form of coping jokes tinged with tears.
Comparing the two is like trying to compare Bojack Horseman to Hamlet (sorry, they're the only two that came to mind), They're both incredibly sad and depressing. One's just funnier about it than the other.
I don't have anything to add here. Good analysis