The difference is a consumer can decide to spend and buy the Australian, the ABC doesn't give me that choice, they use my taxes to fully fund it.
Mate, look at how much the various worldwide News Limited papers/TV shows/websites openly are in favour of right wing conservatives. You don't think when those right wingers get into power they return the favour by doing such things as cutting the funding of their competitors or kill programs that may damage them, or look the other way as they openly break the law?
In terms of aviation, look at which news websites demonise pilots as overpaid and lazy, because they only "work" 100hrs a month? Which news websites publish the "we were seconds from death" hype articles? Which sites are running random speculation stories about the Airasia accident (
What happened to AirAsia Flight QZ8501: Seven theories)?
If you think the ABC is to biased (I believe it's a far sight ahead of News Corp in quality) I'll leave you with the words of the great Stephen Colbert:
Reality has a well known liberal bias 