Finland does actually have a private sector for health care.
The difference tends to be in how fast you get appointments for non-critical health issues. If I have a cough I’m worried about, I can go to my employer provided healthcare and speak to a doctor via phone in literally 20 minutes.
The public system atm would diagnose me with an automated quiz and determine my case to be “non-urgent”. I would eventually get a doctors appointment, if I’m persistent and find all the right numbers to call, online forms to fill in, etc.
If the matter is urgent however, the public system takes things very seriously. And private sector doctors will even forward you to a public hospital in some cases, if they don’t have the staff or equipment needed to help you in a particular case. With concussions for example, I’ve just walked into the local ER and been taken care of right away. If you need an ambulance, you don’t need to weigh your life against bankruptcy.
The public system is also efficient (except when it isn’t). That means you won’t always see staff spend their time on bedside manner. Their job is to keep you healthy, not happy (unless you’re there for mental issues). In my experience the private sector has a higher standard for customer service, because you’re not just a patient when you pay for your care. Your satisfaction matters more since they actually care about getting repeat customers.
Meanwhile, public healthcare wold prefer you never come back, which is sometimes a good thing, and sometimes bad.
I use both sides of the system, and as I already mentioned, the two sides inter-operate in many cases. While it’s been a huge mess at times, Finland is investing in a patient-data-management system called APOTTI which lets you switch doctors and care-providers seamlessly taking your patient-history with you. I once got x-rayd by my employee healthcare, then got sent to a hand surgeon in the public sector so I could get the diagnosis from those x-rays the same day. I left the private hospital and walked into the public one like they were operated by the same company. It’s amazing.