The difference is one of philosophy. The Scandinavian systems largely are based on the idea that it is unfair to allow anyone to pay to cut in the healthcare queue given that it is an essential public good.

It aligns everyones incentives when it comes to healthcare funding (as individuals at least). Conversely, while the UK NHS is excellent, the wealthy often "opt out" of depending on the NHS (as well as the state schools), and so have little incentive to support NHS funding (and in fact, the Conservatives were strongly against the NHS until they realised just how popular it had become in just a couple of years after it was introduced).

The Scandinavian model is inferior from the point of view of those who can afford to pay their way to superior care. It is also strongly dependent on a rough consensus on how much health care is worth, as those who believe health care is worth more does not have an easy option for getting more if they're in a minority, and this is certainly a problem.

I'm Norwegian, but I must admit I prefer the UK model - as much as people in the UK complain about the NHS, it's still one of the public services with the highest approval ratings, and so popular it is pretty much untouchable, yet there are "outs" for those who believe they are particularly badly served and it doesn't seem to majorly affect other service allocation in the UK. On the other hand, there are aspects with the UK model that demonstrate exactly what the Scandinavian models tries to prevent: The UK NHS is often accused of a brain drain from Africa and other regions, by hiring large numbers of doctors and nurses away from poor countries.