DD (Y5) and DS (Y8) have been in private since nursery/reception, in a straight through school. It's been fantastic for them, small classes, they are both very sporty and the sports facilities are superb. Having their own swimming pool means even in nursery they had weekly swimming lessons. They've been able to compete against other schools since Y3, in netball, hockey, cross country, athletics, swimming, rugby, football, cricket etc etc which was important to us.
It's worth considering how much more competitive it is to get a private secondary school place - mine have to sit the same entrance exam as external candidates to go through to Senior, but it's virtually unheard of for a Junior School pupil not to pass, so there are essentially 60 places already allocated when external candidates take the exam. We didn't have to pay for tutoring. The wraparound is also brilliant (7.30am - 6pm) as the school realise that most families have two incomes to facilitate paying fees. Lockdown provision was outstanding, a full online timetable from Y1 onwards and they haven't fallen behind at all. There are very few behaviour problems, either disruption in class or with friendship groups. Feedback from teachers is detailed and regular and staff are always on hand to speak, if you e mail them, you will receive a response within 24hrs - usually much quicker than that.
I will echo a PP, in that SEN provision isn't great. Fortunately we haven't had to use it, but speaking to other parents, if there are mild needs, they are great, but they are not set up to deal with severe dyslexia/ASD.
It very much varies from school to school though, we looked at state and private and for us, there was no contest, but that's only comparing our local state schools to the privates and what we felt would best suit DC.