Private care in the UK for ICU is very limited, and by its nature because it doesn't have as much experience of cases, isn't necessarily 'the best'. Private hospitals frequently transfer very seriously ill patients to the NHS because they don't have the capability to deal with the most severe cases to the highest standard. This transfer also involves a degree of risk.
If I wanted the best care in this country at ICU level I would NOT want to go to a hospital that wasn't staffed by NHS doctors and nurses and wasn't on the same site as an NHS ICU.
The reality with covid-19 is that no one really knows what 'the best' care is. There isn't enough research and no one knows the best way to treat a patient. Hoping for the best on the basis of probabilities is the most any doctor can offer.
There is no clinical pathway which is recommended.
That means there is a fairly level playfield in terms of care once you enter the ICU doors.
Everyone is a guinea pig.