For now the biggest difference is that the Public Lands in SA amount to National Park and the equivalent to Vic State Forests which are mostly run by Forestry SA.
Apart from the 3 areas I noted, the rest don't allow detecting. Although wandering with a detector probably won't get you in hot water, digging a hole probably will.
It's either conservation, logging forest or tree hugger tourism (usually at a cost.)
Even up north, it's either private, pastoral lease or indigenous, some of which needs a permit to enter.
Don't forget the Woomera Range, that's a huge part of the State, again very limited access.
You only have to drive around the Vic GT and count the interstate license plates to answer the question, why don't you detect where you live?