The default: split it equally
Neighbours generally contribute in equal proportions to a "sufficient dividing fence", broadly, a standard fence that does the job (often taken to mean a plain timber paling fence). If one owner wants something higher, fancier or more expensive than that standard, they usually pay the difference themselves.
The process
Before doing the work and asking a neighbour to chip in, you generally serve a "fencing notice" setting out the boundary line, the fencing work proposed and its estimated cost. If you build without agreement or a notice, you may not be able to recover a contribution later, except for urgent repairs. If neighbours cannot agree, the NSW Civil and Administrative Tribunal (NCAT) can decide the fence and how the cost is split.
You can always just agree
Nothing stops neighbours reaching their own arrangement, one paying the lot, or agreeing to a better fence together. A quick written agreement saves a lot of grief.
This is general information, not legal advice; for a dispute, talk to your council, a community justice centre or NCAT. If you and your neighbour want a fence measured and quoted, book a free measure.