Objectivity and Neutrality sound like similar things--and I think the big media outlets operate as though they are the same--but they are not and they have dramatically different effects on how journalism [could] work. Neutrality is everything Greenwald describes: it is failing to say an obviously bad thing is bad or that an obviously good thing is good. Objectivity requires mediation that understands facts and counters lies.
I think Vox generally tries to be objective, and sometimes but not always neutral. CNN certainly pushes neutrality often at the expense of objectivity. MSNBC is fairly show dependent: Maddow and Hayes are fairly objective (though with a definite point of view), Matthews is neutral and not really objective (and most likely thinks of himself as such), O'Donnell and Scarborough are really neither but again they take on airs as though they are. Fox is neither neutral nor objective.
Most of the bigger left leaning journalistic entities are more objective than not (fairly easy since most facts align well with more liberal positions).
In the case of journalist as mediator (whether between people as in a debate or just when relaying a story managing to convey relevant facts and appropriate conclusions) objectivity is obviously quite important. For other types of journalism, namely opinion pieces, it seems like it would be less so but that isn't really the case. Even opinion pieces should be supported by facts, and claims of relevance that are both true and appropriate. It's why I have been bitching a bit about some of Krugman's recent pieces, and that's why pretty much nothing on Fred Haitt's crayon scribble page is worth the effort of reading.