IMHO, I dont think there is much difference. Food has gone up heaps in oz lately.
You can shop 'cheaply' if you buy regional (egyptian oranges, iranian stonefruits etc) and in season. What tends to happen is that you find you have so much extra spare money here (compared to oz), that you just buy whatever you want, and dont worry about price. Raspberries at $10 a punnet
etc.
Just paid $27 kg for oz eye fillet (yes, thats eye fillet, not rib-eye. Nobody seems to want the expensive cuts, driving the regular price down?). $6 kg for nz mince. So it's swings and roundabouts. They do tend to touch you for brand name grocery items. However, driving to the supermarket at 30c per litre, compared to $1.50 in oz.........
As funk says, there are plenty of people who never cook their own food, due to the low cost of eating out (or having them bring it to you).