Freckled - a couple of points about your post. It has already been mentioned that Gove is making it easier to employ unqualified teachers. This will make the problem you are describing with subject knowledge worse. I think entry requirements should be stricter.
IMO the difference between state and private schools is not the teachers, but the class sizes and parental support. One of my close friends did her PGCE with me at the same placement schools. We have v. similar backgrounds, teaching style and subject knowledge. After qualifying, she went private and I went state. We use the same exam board and syllabus. (The only reason we were able to was because we became an academy. Prior to this, the government prohibited state schools from doing the IGCSEs that the private schools used.)
Her results are always better than mine on paper. However, her school only has students capable of getting A-B grades, I have A-G. Her value added is 3 levels of progress, mine is between 4-5 levels (this means I am ecstatic when some students get a D when according to government expectations they should be getting an E or F based on progress from KS2).
The parents of her students get tutors in when it looks like they may not get their grades. Some of my students' parents tell their kids (and me) that they don't need to get their grades as they never did and it cause them any harm (or they are going to work in the family business after they leave. It's guaranteed, so they don't need to try).
The range of SEN and EAL is far far higher in my school, with the additional challenge of ensuring every lesson is fully differentiated.
We are both outstanding teachers. Our schools are both fantastic at catering for our students' needs. The only reason for difference in attainment is our intake, parental support, class sizes and government restrictions.