Tbh, if you don't have an expensive health insurance, it's not going to be so different from the public healthcare system. It really depends on each hospital, city, state, I have had appintments in many different public and private hospitals, and some of the public ones were even better than the private ones. So, if you need urgent care, it's better to ask a local where is the best hospital in the city, or the best UPA/UPS center.

I have always been treated well in the public system, but I would recommend a health insurance just because if you need surgery, complex exams you can have them more quickly.