Keynesian vs. Austrian economics

Okay, the two very different worldviews here. With all the corruption going on, I've noticed a lot of people are starting to be more critical of Keynesian economics, and are starting to embrace Austrian economics. Books like Peter Schiff's Crash Proof 2.0, an update of a book he wrote that apparently correctly predicted the 2008 stock market collapse, are selling well.

I am hearing arguments that with total Libertarianism, charity would still be done, doctors would provide free healthcare to the poor but charge the rich, etc. It sounds like paradise, and to me, unlikely. And yet, at the same time, we are having big fiscal crises. An argument that I do think holds a lot more water is that at the very least, the systems we have to try to take care of the poor aren't sustainable forever. Iceland was pointed to as a model country for having both entrepreneurship and a welfare system that helps all its citizens, but only a few years ago, its economy crashed.

I've been told to read a site called mises.org, that is all about the Austrian school of thought and see their articles. Reading some of them, I get the impression that some of their ideas hold merit and others are dead wrong.

What are the two systems like, and where in history have they been tried, and to what effect? Austrians and Keynesians both think each other dead wrong, and each other's ideas dangerous. What are the big differences and why is one particularly good or bad?

We already have a thread for this.