I can't answer any questions about whether medical care is better in the US or UK, as I've always had really good health and rarely see/saw doctors in either country.
4 weeks ago i had an accident, though, and broke my arm in 3 places.
I was seen in A&E on the Saturday, put in plaster, and given pain relief. On the Monday i went to my own GP, got a line to sign me off my work, got referred to the fracture clinic, and got stronger painkillers. On the Tuesday I went to the fracture clinic at the hospital, saw an orthopaedic consultant, got xrays, a new cast, and additional painkillers.
For the last 3 weeks, I have been to the fracture clinic every Friday for fresh xrays to see how the healing is progressing, and will go again this Friday. If it hasnt healed to the consultant's satisfaction, i will go in for surgery.
Throughout all of this, i have not had to spend any money (not even for a prescription), or fill in a single form or have even a moment's concern about how all of this is going to affect me financially or at work. And i feel like the care I'm getting is really good... i haven't had to wait for anything, I've been looked after and kept informed all along the way.
So i have no complaints about the NHS!