I am neither South African or Australian. However, I do have relatives that are NZ citizens that have made the move to Australia. It was mostly for better career opportunities. Australia compared to New Zealand in comparison pays higher in salary. But has a higher cost of living than NZ.
I'm assuming if you are asking if Australia or New Zealand, you don't have a visa yet? If this is the case, I think the first step is to determine which country will have job opportunities in your career field. You might have seen advertisement that both these countries have shortage in a specific skills,etc. However, it doesn't mean there is a job for everyone. I have seen some postings in the internet about people from other countries either moving to Australia or New Zealand and not being able to find a job. Or the salary isn't quiet enough to pay the bills and have to return back to the country they left.
It probably is best if you have an opportunity to visit both countries to make a comparison of the areas in sort of like a vacation/holiday. But this isn't easy for everyone due to how expensive it can be with airfare, hotels,etc.
I applied for an Australian permanent resident and was approved. However, I had not yet made the move. I am finding out that the industry where I have work experience is downsizing and job opportunities have dwindled. Cost of living is higher than what I am used to at about the same salary or lower than what I'm used to for same position. For that reason, I have not yet made the move. But I have visited both countries on vacation. For me, I felt that New Zealand in the area that I visited was mostly a countryside feel.
Australia is a bigger country in size comparison even though a big area of Australia does not have people residing in them. Bigger country and with resources provides opportunities for international countries in wanting to invest their business. Therefore, create more jobs for locals.
Since you didn't mention if you already have a job opportunity lined up, I'll give my experience with getting in touch with a couple of recruiting companies I scheduled with prior to landing in Australia. I think New Zealand probably follows the same process. Most companies require you to have a working visa in order to be considered for some positions. Being visa sponsored is mostly offered to people that fit the specific skill expertise that they need. However, even if you have a permanent resident visa or a working visa, it doesn't necessarily mean it will be easy to find a job. Some recruiters give the excuse that they require you to have local experience. But how would you get local experience if you just arrived in the country? I think what they say about the requirement about local experience isn't always true because I've read about people getting offered jobs without even stepping foot in Australia or New Zealand.
Do some research which country will offer the best opportunities for your skills and expertise. Not for just now but in the long run. Cost of living in Australia and New Zealand are higher compared to other countries.
Lastly, I think one of the decision factors of why people might move to Australia or New Zealand would have to be which one they were able to get the visa from. Or which one took less time to get.