I did this myself, so
Primary School- State
11-16- Private (Day)
Sixth Form- State
I definitely made the right decision. For me it was based on the fact that my school had quite a small sixth form so some classes would have been only 3/4, whereas the 6th form college was very big, so classes were c.15.
Also, I think that the sixth form environment- (no uniform, we only had to attend for lessons, there was no hot housing, if coursework wasn't handed in you weren't chased- just got a zero) really prepared me for studying at Cambridge where I only had 1 hour of mandatory contact time a week. I was already used to organising my time and motivating myself. However, my sister did the same thing and didn't do very well at A-level because she didn't really adapt to the lack of structure, so it depends on the person I think.
On the downside, the minimum requirement for studying an A-level at the 6th form college was a C at GCSE so the classes were, to put it mildly, very mixed in terms of ability- pretty high failure rate. I didn't have many peers within my classes (I know that sounds arrogant but it was true). I definitely wasn't stretched beyond A-level standard so I did find the first year of Uni quite tough in terms of getting my critical thinking to a higher level.
My decision was made easier by the fact that my private school wasn't particularly great anyway- non-selective, teaching a bit mixed.
On a more cynical note, the top universities are trying to improve their intakes from state schools, and the stats only look at "last port of call" so to speak, so applying from a state rather than an indy could help him.