Taking what you said at face value - this doesn't give an advantage to either system when it comes to the minority of people who have complex health problems. I

Taking what you said at face value - this doesn't give an advantage to either system when it comes to the minority of people who have complex health problems. In practice, European private healthcare is likely to have more price transparency and cheaper costs due to the pricing of procedures and medical consumables having been negotiated/capped by a government agency or an independent body.