Both of the two systems have pros and cons.
For the universal system, the advantage is it open for all citizens. Everyone has the right and equal chance to access health care. It’s the most beneficial for the middle or lower class and labor. It can increase labor productivity. However, in the universal system, the doctor and nurses lack motivation by higher income, their attitudes toward patients are based on individual. The efficiency of public health care is also not ideal, there are limited resources for the whole population. People could be waiting for the treatment they need that is unavailable for a long time, and die without any treatment.
For the private health care system. People get what they pay for. Most of the private health care systems are more expensive than public, people pay for the insurance companies to cover their medical expenses. The doctors tend to use the best and now treatment for their patients because all the high expenses will be cover by the insurance. The elderly group is more favorable and less favorable to this system at the same time. It can give them the best health and medicine they need, but it isn’t available for everyone.
In my opinion, these two system could work the best when you combine them together. They complement each other. The private system provides quality equipment, good medicine, and advanced treatment. To make it available for more people, the government needs to set up funding to aid people to pay for their insurance.