As for US vs UK treatment, having spent 2 weeks in hospital in the US with my SO having major surgery, i think i can say the treatment on the ward is more or less the same, the big difference in the UK is you worry about the choices (or lack of) you have as its more or less prescribed institutional care, vs in the US you have a constant request for your insurance data and ongoing worry if they will cover the ever increasing bill which they didn't confirm until 2 weeks after discharge. Ok so it was travel insurance and emergency care but not knowing if the $85,000 bill would be taken care of or if we would have to find the money was rather concerning all the time i was supposed to be taking care of my SO.
I also wouldn't take trans care as an example of NHS care. Its a tiny niche of treatment which is under staffed and neglected for too long which is bad for all of us trans people but not really representative of the NHS as a whole. But as i said the NHS is institutional and you follow the process, and more or less private treatment mirrors NHS treatment with the same Dr's and procedures, you just skip the queue and get a nicer room and free coffee in the waiting room