I do think that there are indeed two separate issues here - I mean there are probably loads of issues, but there are two important ones here that are often mixed up in people's minds. So yeah, with news organisations I think it's important to consider the impartiality or otherwise and also the quality (I'm including corruption within that for these purposes as I think it has a bearing on the quality).
So thinking of UK newspapers as something I know relatively more about. You have on the right; Times, Telegraph, Mail, Sun... and some others that slip my mind just now. Then on the left you have the Guardian and The Mirror. And there is a newspaper called The Independent which claims to be neutral but which to my mind is really more left-leaning. So all of those partialities are acknowledged and not really disputed (with the possible exception of the Independent). But in terms of the quality of the reporting I would say that The Guardian probably is the highest. Times and Telegraph have both been traditionally high too, whereas The Sun is an absolute shit-rag and The Mail has a horribly tarnished record going right back to when it supported the Nazis before WW2*. I actually don't know to much about The Mirror or the Independent but I will say that the former is a tabloid whereas the latter at least aspired to be something of a higher quality.
Anyway, above I mentioned the Telegraph and Times and to me they represent quite a dramatic change in that, when I was growing up, my parents (being home counties Tories, or worse actually, aspiring to be that) naturally took The Telegraph which at that time was a decent newspaper, I might not have agreed with its editorial line and it might have seemed weird that the letters page was dominated by retired majors from Surrey, but the bits at the front where it reported news tended to be truth and correct. And even the editorials might make arguments and not those whose conclusions I agreed with, but they tended to be based on factual statements and the arguments had more to them than demagoguery and thinly veiled attempts to push the owners' line. And I think the same for the Times. But now the Barclay Brothers just use the Telegraph to write what they want, the standards have irrevocably declined and it well documented that they spike stories so as not to annoy people they want to court or, famously on one occasion so as not to lose advertising from HSBC. It's really shit but dangerous shit cos Mum and Dad still think it's a newspaper and it's not any more. It's actually quite sad I think. But yeah it's a perfect example of something that was always partial but once had high high quality and now does not.
I think that The Times is similar in that of course it now pushes Murdoch's line. But, it seems strange to say it, I actually think that compared to the Barclay Brothers, Murdoch has some kind of standards, and he doesn't quite take the piss to the extent they do. As a rule his news outlets push for deregulation and so on, but I think that probably is something he believes in (and which happens to make him money), whereas the BB have no particular beliefs in that way beyond selfish accumulation of money.
*As an aside, one particularly astonishing episode was a few years back when the Mail made a number of vicious personal attacks on the father of Ed and David Milliband who were both influential Labour politicians. They claimed that he was essentially a traitor to the UK, I think because of a single diary entry written when he was 17, per wikipedia "On 27 September 2013, the
Daily Mail published an article disputing Ralph Miliband's patriotism with the headline
The man who hated Britain" It seemed utterly crazy to me that a newspaper should choose pick this fight and then try and make its point by raking up a period during which it originally supported Hitler and the British Union of Fascists while its target - a Polish Jew - was first fleeing Belgium and then volunteering for the British navy where he saw three years of active service - and yet this sort of mendacious and hypocritical nonsense is entirely typical. And worst of all is that they somehow got away with it.