Based on a small sample (one!) I would disagree with Talking. DD did poorly in the 11+ exam at the nearest super-selective, consistent with her relatively low CAT score, coming in the bottom third of the 1000+ applicants. She did not take SATs but was not an academic star at her Prep.
Five years later and grades for her 10 GCSEs should be at least as as good as the average for the Grammar, and she is confidently expecting to gain a place on a popular course at a good RG or equivalent.
Part is good teaching, and smaller class sizes, but a lot has been confidence building both by academic and extra-curricular staff. Learning support at her school has been fabulous, and indeed an eye opener for her to discover the problems some of the other pupils are struggling with. It has been lovely to see her start to believe that she can start competing academically and start having ambitions.
Her school takes a good proportion from the state sector at 11+ and based on coffee morning complaints about various tutors, my guess is a good proportion of those also tried Grammars and failed. Given results at her Indi are better than the Grammar I think it is reasonable to assume that the Indi is providing better value added. The Grammar, being free, will be far more selective.
The sad thing is that had my daughter remained in the state sector (leaving aside the fact that the state school she was offered was not one we applied to and was pretty troubled), given her low CAT score and relatively low attainment at 11+, could well have been given low targets and got lost.