I’m speaking from my personal perspective as I’ve lived in Cambridge most of my life, went through state school system, had family /friends who went through independent sector and now have a child about to go into (state school) primary. I’m a professional.
Pick where you will be happy to live don’t base it on schools. Wherever you live in Cambridge the secondary schools are very good: Netherhall and Coleridge are the poorer performers but honestly it’s all relative as Cambridge has some of the best states schools in the country. Things also change - 15 years ago Netherhall was the most desirable school.
I don’t think it’s a problem sending one child to private school if that’s what is right for them. My family sent one child to Perse because he was very clever and the other child went the state school route - was absolutely fine. I think that’s really normal around here. You need to be very bright for the Perse. No point sending a child who is not going to respond positively to the academic culture. Btw - both are successful adults - Perse grad is leading in his field, other child running own successful business. It’s all about giving your child the best opportunity for them. If they’re into performing arts then for example, pick a school that excels in this.
We have lots of good state primary schools not so many outstanding but things do change overnight. The vast majority are very good schools.
In my personal experience, Cambridge gives children the opportunity to be surrounded by a mix of children - aspirational peers, international backgrounds, different cultures, British born families from mix of socio-economic backgrounds. That’s positive for kids to be exposed to such a mixed community in my opinion. It will be more homogeneous/ international at independent schools. But wherever your children go, they will be exposed to positive peer pressure and this I truely believe is what makes children want to achieve. Teachers here are also on the whole very good and intelligent. That’s generalising, but as cambridge is such a nice place to live, schools have no problem attracting the best teaching staff.
I don’t know anything about Perse entrance exams. In terms of extra tutoring I imagine most ‘middle class’ kids at secondary schools here get it - that was the norm at my school over 20 years ago. Can’t imagine that’s changed. It’s also very normal to do extra curricular activities.
Honestly if I can’t imagine spending my money to send my child to private school as the schools are so good here I have confidence that she would achieve the same outcome. If I lived in a different part of the country, I might feel differently. But I came through the Cambridge state school system and work in a highly skilled profession alongside many people from leading independent schools. The only thing they have that I don’t is a natural air of confidence - I have to work harder at that!
Hope that helps and good luck with your decision 