Looking at the summary Aga posted upthread it looks like a larger difference mid-grades (like a normal distribution graph?) which suggests that the AAA will succeed anywhere, the EEE will not hit the heights anywhere but the smaller classes, etc may pull up those in the middle.
This confirms what I have always believed about private education - that it adds some value for kids who are average or just above average, but makes little, if any, difference to kids who are really bright, as they will tend to do well anywhere.
I think it's certainly true that we need to look more at the inequality within the state system - not all state schools are created equal! (Having said that, I'm not convinced that all independent schools have an equal offering either!) Kids with educated, supportive, aspirational parents will tend to do well regardless of school type. Kids without that parental support don't have an even playing field. The tools that universities currently use are pretty blunt - you can only tell so much from someone's postcode!
I think it's very clear that there is a huge difference between degrees from different institutions, and I would agree that most employers know this, but horse is quite right to say that this needs to be more transparent - the lack of transparency just perpetuates the inequality in the system. Kids with parents who know how the system works will inevitably guide their children about which subjects to take, which universities to apply to and so on.