None. They don't talk about it. They stopped publishing exam data by school type in 2017, if you want to find this now you have to make an FOI request.
In their 2022 study into the factors affecting outcomes they avoid references to school type in their executive summary, discussion, and conclusions, despite the fact that it was as significant as the factors that they do discuss, at length.
https://www.cao.cam.ac.uk/files/attainment_outcomes.pdf
But if you move from a position where students of type x and y perform equally well - because the admission system is type-blind and considers only ability - to a system arbitrarily designed to admit more x and fewer y, then predominantly lower calibre y applicants will not be admitted, raising the average ability of y students that survive the admission process. Even without moving the bar for x at entry - lower GCSEs at Oxford, and lower UMS in old money at Cambridge - a performance gap between x and y will emerge.