I have public insurance and have been in hospital 5 times - 3 times for 5+ days. The care was very good and I suspect not all that much different than private insurance. My daughter, who was 7 and 8 months was hospitalized for pneumonia and croup.
While my daughter was in hospital, I was automatically given a bed next to hers and free meals. On her 2nd day, *I* became ill and was told to go to the ER on the adult side. It was a Friday night, and right away I was seen, vitals taken, bloodwork, an ultrasound done, an x-ray, another ultrasound by a specialist, and admitted overnight on IV. Now, it was no emergency - I had a bit of a temperature and low BP but in the end it was just a GI infection. That said, there are rare circumstances where those symptoms COULD have been serious but i know on public health care in other countries, I probably would have been sent home with 'stomach bug' listed as the diagnoses with no where near the tests (and speed) that I was delivered.
When I was in the hospital having my daughter, I stayed 6 days and was given everything I could have asked for - even back massages from the nurses.

The HEAD OB delivered my baby. On postpartum, i got 6 weeks aftercare with a midwive, breastpump rental for 6 months.
When my daughter had pneumonia, we were sent home with a very expensive nebulizer machine - all covered by our public health care.
Suffice to say, in the 3 years I have lived in Germany, we have not once had to pay out of pocket expenses for anything medical - not one ultrasound, not one drug - not even the Kamillen bathing stuff for after giving birth.
I've stayed in 3 different hospitals here and all have been really clean, well-staffed and attentive. So I'm totally pro-public health care in Germany
Now the only thing with my daughter is that we did not have a private room at first. We had another baby and mother in our room and my daughter could not fall asleep with the noise. I was REALLY desperate to get her to settle down considering the night we had so i BEGGED the nurses for a private room. I even tried to bribe them. The next day, they arranged a private room for us (and no, they didn't take the bribe

), I'm not sure if it was because I was so desperate, or if it was the nature of my daughters illness and i'm also not sure if we would have had a private room anyways if we had private insurance as the doctor alluded something to that effect.
That said the 'non-private' rooms were never bad. I never had more than one other person in the room and never had any long waits for anything.
sorry so long - thats my experience anyways. Private health care here kind of scares me because if you ever need to come off of it, for whatever reason, you cannot sign up for public health care unless you have been free from the private system for one year. Don't ask me how that works, thats just what i was told and could even be wrong. But i have a friend who's german husband had private before they married (she's british) and it caused some problems with her getting public, etc.