Thanks for the link.
That blog post was actually not a good example of Rosenberg being mentioned only because Greenberg was.
The pairing of the two critics was the Jewish Museum's frame and the post was responding to it.
From your discussion (and the Jewish Museum's) it seems that Rosenberg was more interested in evaluating artists (are they heroic? cosmopolitan? a good embodiment of Marxist ideals?) than the artwork they make.
There is a strain of art that values personality and anecdote over work and it may trace itself back to "American Action Painters." But it's a bit like basing jurisprudence on the lives of the founding fathers and mothers rather than the study of history, economics, and so forth. Fun to read but incoherent if your goal is a common language.
You can compare work to work but it's hard compare artists to artists so you get careers based on personal funkiness, e.g.: "The most important thing about Tracey Emin is...well, her Tracey Emin-ness."
see also, Tracey Emin, Fame Academician (hat tip Marisa Olson). A feminist reading of Emin can be made and that writer doesn't even try, and there are certainly worse artists currently stroking personality cults (for example, Richard Serra).