My phone just ate a long message. I'll write it up again later, but in short, I had my first baby at home with NHS midwives and the second with independent midwives. I saved up for a year before getting pregnant, and paid in instalments, and it was worth every penny. I had long appointments during pregnancy which covered all sorts of birth and childcare preparation and debriefing stuff about the last pregnancy and birth as well as medical care. DPand DD were included. I felt as though I'd been able to consider all sorts of options, not just the best case scenario.
For the birth itself, it made a huge, huge difference having a midwife at the birth who I knew and trusted. At the time, my perception of things was that my midwife hadn't done anything medical at all and just supported me, but when I read my notes afterwards, I realised that every time she'd given me supportive, reassuring, pain relieving touches, she'd been very discreetly monitoring blood pressure and hear rate and stuff like that without me even noticing. The birth was amazing - I could really feel the difference giving birth without a stranger present.
The most noticeable difference was actually in postnatal care. I had regular visits, keeping an eye on my health and that of the baby for 2 months after the birth. They helped me with breastfeeding, recovery from the birth, baby health problems- in many ways, the cost was worth it for the postnatal care alone, which was at a level that the NHS really can't do.
My only regret is not having had my independent midwives for the birth of my first child.