I've never been to either, but I was under the impression that in both Australia and NZ, there were lots of critters willing to bite/sting you without notice.

I know that a lot of countries on earth have nasty little things lurking around, but is it really that much more dangerous in Australia than in NZ then?

Yep they're quite different. In NZ we have some supremely ugly insects (http://www.themarysue.com/record-breaking-giant-weta/) but they are harmless to humans. No snakes, crocodiles or anything like that. You can walk barefoot in the outdoors with impunity.

Perhaps you could get taken by a shark if you were very unlucky.

Wow. That's definitely news to me. It's really cool, especially considering how close Australia is (compared to everything else at least).

Uhmm...definitely need to go visit some day.

Australia has more than its fair share of poisonous snakes. http://lifeinthefastlane.com/when-doug-met-struan/ is an excerpt from Last Chance to See by Douglas Adams. Douglas discusses poisonous snakes with Struan Sutherland.