Re Broomwood, I would like to emphasise that my child was very happy and I can't fault the pastoral care aspect of it - something I am missing in the secondary school. I also think Mrs Jenkinson is a great headmistress with spot on advice who knows all the girls incredibly well.
However, it's definitely not as academic as it could be and doesn't do much for the brightest girls at the lower end of the school. They do have a scholarship group for 13+ big not really anything for the 11+ group.
I am surprised to hear that focus on 11+ is increasing - from the destinations list and number of girls leaving at 11 vs 13, I wouldn't arrive at this conclusion. Something to probe, but in any case there will always be a dichotomy of the split departure point.
I think Broomwood is serving a very clear demographic and that demographic is aiming at 13+ boarding at Benenden, Bradfield etc often with boys at Northcote Lodge aiming for boarding too.
Re academics, I think Northcote is definitely more academic - this is consistent feedback from parents with kids at both schools.
At least half of the group at our 11+ group had tutors (sometimes two for maths and English), the others might have had them too but I didn't know the parents well enough to be certain. That's said, I don't think it made a difference to the outcome - the academic ones got offers from alleyns, jags, whs, phs, Wycombe abbey. Less academic - streatham and Clapham, Emanuel, woldingham etc. Tutoring didn't seem to make a difference. But people still tutor. School prep on 11+ is in a different league to pure 11+ schools (I am comparing to West London preps) - the latter ones are more thorough.
Rehomework at school, I hate this - removes flexibility and gives you no insight into what your child is covering at school and what their weaknesses are. But then I am a control freak.
All in all, very happy with our experience and my child is doing very well in secondary school - she was very well prepared, especially when it comes to humanities. But if I were doing this again, I would have chosen an 11+ school with more mixed demographic. I am struggling to think of any schools apart from Hornsby though that would give a better experience than Broomwood.
Ps if you don't get what you want at 11+, you can always spend another 2 years at a 13+ prep. Broomwood and newton prep (and Fulham prep further afield) always get kids for year 7 & 8, either because the families want boarding at 13+ and need to close the gap (e.g. Coming from font on, Honeywell, abroad) or trying for better schools at 13+ when the child is more mature. Ultimately, you need to go with the school thAt feels right and as long as you are fully aware of the trade-offs, strengths/weaknesses you should have a good experience)