Private health insurance is just like any other - it is an insurance company and they will take your money but be slow at handing it out.
You could end up paying thousands of dollars then be let down when you need them. Importantly, know that there are always out of pocket expenses when using private cover and these can be very high.
Waiting lists may be a factor to consider but if one is very ill (like heart, brain, broken bones etc) the public system gets you done quickly anyway.
Your age and other medical issues which are in play or may come up in time may be factors to consider.
If you have been happy with the treatments provided at your local health services then stick with them.
Good luck with your decisions. Anne