I'm US citizen who lived in Germany for a couple years and had German health insurance. I would say that the access to care is overall better, but Germans, being who they are, have a talent for both bureaucracy and efficiency.

In my time there, I had a trip to the ED for a broken bone and a virus that put me in the hospital, plus a couple normal doctor visits.

Absolutely everything was covered by my insurance and wait times were about the same. The only real difference in the care itself was that there were a lot more patients per room and there were fewer frills. The ED had a large room with at least a dozen exam chairs with curtains and my hospital room had 6 patients in it.

Personally I'd trade a private emergency room for no copay in a heartbeat.