I've tried tellings doctors in Denmark I wanted X, Y, Z test and getting told, nah, the outcome wouldn't change your treatment so we don't want to order those tests.
Generally, healthcare is decent, but no doubt a good PPO plan does not compare :)
Public health care seems more like HMO, you have to use a provider within network. Sometimes you need a referral from your primary physician, etc.
You can pick your doctor, but not everyone can take on more patients.