Over time Australia has a 28% win ratio over New Zealand, if anything the rivalry between Oz & NZ is actually pretty new, probably mostly due to the non-rugby migration treads between the countries.
But then again what defines the biggest and greatest rivalry? There seems to be a mixture tribalism, historical, socio-economic & rugby results in people's posts.
England being in the poll 3 times is a classic example of this. As they stepped on many toes through world history.
Long historical history with France for good and bad reasons, mostly bad. To a lesser extent same with Australia, Ireland, Scotland and South Africa.
Historical tribalism is evident in the Wales-England rivalry, which at least sparked it, in rugby terms they both have a 45% win ratio against each other (England just 0.38% ahead), the remaining 10% ending in draws.
That's the closest rivalry in world rugby.
BUT they both not world beaters in rugby terms so it deludes it slightly, much like if Russia-USA & India-Pakistan played first class rugby against each other.
If you cut out all the emotion and the other factors I mentioned before and go on pure rugby reasons, South Africa vs New Zealand is the biggest. Period. Today, like most of the 100 years of rugby history, it's been SA & NZ swapping between number 1 & 2 in rugby.
BUT then again rivalry is relative to people. Each to their own. Tell a Welshman he must be more excited for a SA-NZ than he must be for a WAL-ENG game, because technically that's the big game of the year. He'd knock you out with his shovel
EDIT: PS I got stats from
RugbyData.com