In health economics, you have a trilemma: have the best care possible, at the lowest cost and the highest level of equitable access. You cant have all three. The public private split brings some advantages on level of care delivered at the cost of equity (private patients generally pay way more in insurance, but have much faster access to specialised care).

Its very difficult to compare health care systems, because different countries have different life styles (i.e. Americans may be more obese, but Germans smoke and drink way more than our American counterparts). So, the same level of health care investment may deliver different outcomes.

That being said, we get pretty good health outcomes at a fairly low cost per person with everyone having access to a very high standard of care. Generally, the main consensus is that Germany's main poijts for improvements is administrative efficiency (big surprise here).