Private much more comfortable, clean, quiet, noticably higher staff-to-patient ratio. Think of it as a hotel.
Consultants are very likely moonlighting from a major local NHS hospital, they might arrive with their golfing shoes on, and will turn up at set times. At certain times of day, and during the night, it will be mostly unstaffed apart from a few nurses and one (relatively junior) doctor.
I had the misfortune to have quite a bad accident and was airlifted to a major regional NHS hospital. Emergency care, operating theatre, anaesthatists, pharmacists, physcian, surgeon, theatre team and stores were all available to put the bits together. ITU, couldn't fault it. Nightime emergency consultant brought up from A&E when I went downhill a bit.
When I got sufficiently better to care, I noticed that the small ward and barrier nursing room I ended up in were not very luxurious.
Private is more comfortable for scheduled, routine repairs.
Some parts of NHS hospital care, especially for the older patient, are disgusting.