There is now some data showing one way CNN is biased --Breitbart and Fox News seed the media environment with disinformation, and eventually mainstream outlets pick up that disinformation. (Torture is a good example - the right really wanted to bury discussion and largely did).

http://www.cjr.org/analysis/breitbart-media-trump-harvard-st...

Another way to say this: only one side is willing to blatantly lie. Luckily media outlets are starting to realize that and moving to coverage of the truth not just what people say.