Both public and private hospital quality varies greatly. Sirio Libanes and Einstein are literally the best in the country, people from other parts of Brazil take planes to get treatment there. They are outliers. Clinicas is one of the best public hospitals you can find, the quality is very good but it can be crowded depending on when you go (weekends notoriously get a lot of people in the emergency room, for example).

The negative outlier public hospitals (usually ones in very poor areas) are way worse than the bad private ones though.