In New Zealand everyone over 65 gets the age superannuation (Social security?) even multi millionaires but it is taxed. I get an extra supplement because I live alone. Because of my other assets I do not get help with rates, electricity etc. We also get a gold card which gives free local transport (out of peak travel times) and many discounts in shops etc. I get 5% off all my groceries (not alcohol) at my local supermarket on Tuesday and Wednesday.
In Australia you get the aged pension at 65 (it is going to go up to 67) but it is means tested so you have to give details of your assets and income. Because of my recent trip to Europe, my assets have gone down so I have sent my changes to Centrelink in Australia and they will now give the NZ government more money on my behalf but it is not as much as NZ gives me and I have never done a day's paid work in NZ.
If I still lived in Australia, I would not pay any tax and as long as I was eligible for any pension even a $ per week, I would get rates and power assistance plus free driving licence, car rego. I still have my Australian Seniors card so get very cheap city transport but not free when I visit.
However medical care is much cheaper in Australia. I need the cataract removed on my right eye but as my left eye is so good, I cannot even get on the waiting list for free surgery in NZ so I am going private and will have to pay about $5000. In Australia, I could get it done for less than $1000 or even free if I was prepared to wait a while. I have thought of going back for the surgery but would probably have to live for a month or more with my sister and my Brother-in-law and he and I would probably come to blows.