Anecdotally, the best system I've ever experienced was in Austria, which is some weird mish-mash of public and private which I never fully understood the details of. You have to have health insurance, but those companies are non-profits... or something like that. Here in Italy, it's government run, and suffers a bit from that, at times, although on the other hand, you have complete "peace of mind" in terms of not worrying about losing your job or something and being unable to take your child to the doctor.