Dear OP,
There isn't a general rule.
You need to judge on a case by case basis.
All things being equal I would prefer the state option to the private option.
But in many cases everything isn't equal and in some cases the state provision may be so far below what you want for your children that you choose other options.
OFSTED is only a guidelines: I recently visited an Ofsted outstanding school that made me depressed (kids filling in pages of worksheets, targets on the wall, no space) and there are Ofsted satisfactory which are warm and friendly and high on pastoral care and might prioritise exploratory teaching over SATs results (in our borough, harder and harder to find).
And all private schools cannot be lumped together. I looked round four, and i'd only send my children to one of those. One I hated, and one I liked but not enough to spend the fees. One was OK - and the last seemed like a normal, friendly school, but with more opportunities and room for individual attention than the state options available (and if we'd got into our closest state school I wouldn't even have been looking).
Re spoilt, public school types. i really think it depends on the school. I don't think I fit that image, and yet I was private school educated. I don't think it's fair to generalise, any more than it's fair to generalise about chavs in the state system. Both are objectionable stereotypes.