(The Wikipedia article on German Health Insurance is quite good. The Bundesministerium for Health publishes some articles in English as well as being thoroughly descriptive in German. Here's a good article from the American view on the system.)
What is unusual is having been on private insurance for the last 4 years and then moving into public and thus being able to directly compare them in this way. To be allowed to move into the private system in Germany, one needs to make a certain amount (50,850€ in 2012) and the move is one-way: like a roach motel, you can enter but then you can never leave. That is, you can reduce your income for over a year to below the threshold, but most people in the situation where they would want to change back— getting married, having children, getting old— couldn't afford the loss.
Also, after the age of 55, as far as I know there is no path back into public, so even losing one's job in a country where age discrimination is rampant could leave one facing an increasingly unaffordable insurance bill.
However, in our case, we have had American expat(private) insurance as my husband was seconded here and therefore we were allowed to have non-German insurance. When he moved to the German firm at the end of the year, we needed to make a decision as to what insurance we would move to. Complicating the issue, 1. he had never been previously insured in Germany, so could not return to his prior public (he left Germany while in school and covered under family insurance), 2. the law in Germany did not allow non-EU nationals from countries without public plans to enter into public if they would not be ordinarily eligible.
This was such a stressor that we considered moving to the Swiss firm or the British firm, either of which would have allowed us to enter immediately into the national health schemes. The difference in cost between private and public here in Germany, for our family with a non-working spouse and two children, was such as to make our remaining here unaffordable, as well as seriously disadvantaging the children. We got as far as discussing the advantages of moving when there was an anticipated revision of the law to allow workers the one-time opportunity to enter public if they had not previously been insured in Germany and it was determined that the German's previous private cover (by his parents' insurance) did not count.
So, in my time here in Germany, as a private patient, I have had: unscheduled emergency surgery, standard things such as mammos and colonoscopies, emergency room visits for breathing issues, pneumonia, specialists, MRIs, dermatology visits and ordinary and specialised vaccinations. My kids and husband have had the standard, with a sprinkling of allergist, dermatologists, and so on.
Before we moved to public, we talked to all of our doctors and to our dentist (whom we adore- he is the best we have had in years). They all assured us that there is no difference in treatment between public and private patients, other than private versus public room certain other clearly defined differences: Germany sets a minimum required amount of coverage, all insurances adhere to it, and differentiation is in the extras that are given.
The minimum is quite generous: if I could have paid less by taking out acupuncture and other non-scientific remedies, I certainly would have. Germany invented the quack science of homeopathy and although there is pushback against the public insurances paying for it, many insurances do.
Next part- what we chose, why, and how the execution has gone.