Realise I'm quite late to this thread but have input as someone who left Bablake ~ 15 yrs ago. I know a lot can change in 15 yrs but this is an honest review. I also know people who went to King's High and Rugby. The first thing to say is Bablake is better than KHVIII :) in both academics, sports and generally everything, so if you have a choice go to Bablake over KHVIII.
Academically, most of the teachers were passionate about their subjects and were good at teaching. There were a few teachers who were less competent academically and pastorally but they didn't last long. Good results were pushed and we were encouraged to challenge ourselves. For people who were intrinsically motivated to do well, this was fruitful. I was one of the smarter ones who got great results and a destination Uni and I believe the school challenging me appropriately was a big factor in this. Having said that, there was a large portion of the student body who were either bright and motivated but not in the top centile of the very clever, and also many who were smart-ish (a few As, Bs and Cs) but not particularly motivated as they were going to take over the family farm after leaving school, or Daddy was more interested in taking them to Costa Rica in term time rather than them staying in class. For the motivated and clever ones, this was frustrating, as particularly at GCSE level this slowed up classes as teacher time was spent pulling others up. That being said, there was a lot of opportunity for extra stretcher classes or teacher interactions outside of hours. At A-Level this improved as classes were smaller and people more motivated, and not everyone got into the Sixth Form. Back in my day Russell Group Unis and Oxbridge were encouraged as destinations but now I know they also focus on degree apprenticeships as well as alternative routes post school. Those who I knew that were highly motivated to go to Oxbridge all tended to get places and there was mock interview support for this plus taster days. This is likely to be more difficult now because there's much more of a push from OxB to take state school pupils.
The SEN provision was okay but not excellent but there was never quibbles about extra time in exams etc. I am not sure if the learning support department did more harm than good. All the staff who were there in my time will have left by now though.
The extra curricular was great, there was always something to get involved in whether for fun or competitively. The teachers who ran their respective extra curriculars all enjoyed them. This was a particularly good experience. There were many opportunities for travel on school trips although of course these cost extra.
In terms of culture. Cleverness was definitely admired by the teachers and the other pupils, particularly in the later years. There was bad bullying but I think this is the case in many schools. Unfortunately the people who were bullied were not necessarily suited to the competitive environment. There was a few major incidents which were dealt with effectively when parents got involved with the school. I am not sure how much was done without the push of parents - it was quite a free range culture (perhaps too much) where pupils were expected to develop their own resilience. I have been told that the pastoral care and safeguarding is much better now. There were a few edge cases of teacher pupil relationships - one teacher getting into a relationship with an ex pupil just after she left, and also one with a current teaching assistant - but I believe that has been clamped down on now.
It was a diverse student body and a lot of pupils from lower income families. What you get is good for the fees.
The girls (now women) I know who went to King's High are all very ladylike and demure (!). This is different to Bablake which was more free range / a little boisterous where the girls gave as good as they got. Rugby is a traditional public school so I don't think it's really comparable to Bablake or King's High.