I see this thread is a couple of months old but thought I’d add my thoughts anyway.
Firstly sorry to hear about your miscarriages OP.
I’m a primary school teacher and have taught in both state schools and independent prep schools.
State schools offer the benefits of mixing with a wide variety of children, including children with additional needs and from a wide variety of backgrounds. However naturally teachers have less time per student and there are less resources.
Prep school offers the benefits of more attention, lots of extra activities, Specialist teachers for languages sports etc, but are not immune to bad behaviour, bullying etc. They are also not a ticket to having a super high achieving child.
Broadly I would say the teaching quality in both settings was similar. Independent schools tend to buy into more teaching schemes so the lessons were consistent but not always creative. State had less resources but lots of young newly qualified enthusiastic (cheap) teachers.
I would say the most important thing to consider is whether your dd would be well suited to the independent environment. It is super fast paced, high expectations and sometimes a little tough. Unfortunately I taught a few children who, although had passed the entrance exams, really struggled to keep up.
As a side note, in my classes in the prep school there were a high proportion of only children.
I’m sure your LO will be fab wherever they go to school x