thebestisyettocome you're not contradicting me at all, as I said, bright, motivated children will do well anywhere and, given this, it is perhaps the less bright and motivated who are likely to benefit most from the additional support available at private schools.
That is what I observed amongst my peers. Bright able children did well in either sector and have secured excellent jobs. Some less able children who might have been a bit lost and sunk below their potential in the state sector were probably helped to achieve more in the private sector. In state schools some did sink, others didn't. This begs the question, for a bright, able child, why pay extra when they'll do well regardless?
To put it another way OP, consider your children, their needs and learning styles. Find out about the schools in your area, their ethos, style and what else they offer. Work out which offer the best match. If there's not much in it, why pay considerably more for no guarantee of better results? You might even find that a state school offers a better match for your child's needs, personality and potential.
I do think if your experience is all private sector, you need to find a way to feel confident in and proud of your local state schools, if they deserve this of course (some are dire, I'm not defending those), so that using one might feel like a positive choice. That comes from being able to identify with them in some way. Talking to people who have had a good experience of the state sector might help. I think your original dilemma is about lack of familiarity, so feeling more comfortable sticking with what you know. You know that's not an objective basis for making a decision. So, how do you achieve objectivity? Only through knowledge and familiarity, preferably gained through people you know and trust.
It is my familiarity with the state sector and the good experience it can offer that makes me feel proud and happy to offer that experience to my child. Because I think this offers things the private sector cannot, I would feel sad that she was missing out on something positive, if for some reason I felt that I needed to send her to a private school. That's essentially the mirror image of your experience. It simply demonstrates that pride and confidence in the state sector is possible - so that perhaps there is no need for you to feel that this must be second best, just a different good experience from the one you had.