In the public system, prices are set according to the Medicare Benefits Schedule (MBS) and Medicare pays 100% of the cost. You won't be left out of pocket, but you won't get your choice of hospital, doctor or appointment time either. In the private system, prices are usually higher than those listed in the Medicare Benefits Schedule and Medicare will only pay 75% of what it would have, had you gone public. Your private health insurance covers at least the remaining 25%. If your private doctor charges more than a doctor in the public system, which is usually the case, you'll have to cover the extra expense.
Remember, with hospital insurance, you'll also have to serve waiting periods. For example, if you have a pre-existing medical condition, you'll have to hold your policy for at least a year before your cover would chip in towards the cost of treatment.