"Old" atheism = quietly sitting in the corner, keeping it to yourself.
"New" atheism = not quietly sitting in the corner, keeping it to yourself.
That's pretty much it.
It's not like Prof. Dawkins has found a cutting edge way to not believe in gods, or Mr. Harris has broken new ground in disbelief, or Mr. Hitchens is in possession of an innovative manner of unbelieving, or Prof. Myers has distilled a previously unknown debunking of the supernatural mindset.
They, and others, are just talking about it, and we have the technology to know that they are talking about it. Often at the moment they talk about it. And their talking about it has made others who also disbelieve less afraid to talk about it.
Though, in geological terms, I am a "new" atheist, having only been one for about 20 years. That's not even half a blink of an eye in the roughly 4.5 billion years the planet has been chugging along without the aid of Odin or Zeus, Yahweh or Baal.