Short answer. In nearly every case. Yes. If you live in the Western Suburbs and their peers are going to an Independent Public school, if your child is top 5% academically or has an disability, you have personal history at that school, if your local public school is going through a difficult transition or if you are looking for religious education as part of the curriculum then maybe not.
Long Answer. As a teacher supportive of public education this was a very difficult decision and long drawn out process for my own children. For a short period I was teaching in a public school, was an advocate for private education and was sending my children to a private school. It made it very difficult to recommend a state school to parents and raised the question of "if I believed in the private system why wasn't I teaching in the private system too?", "Was I not good enough to even teach in a higher SE school and why wasn't a public school good enough for my own children?"
I wanted the best for my kids as do all parents, the independent private schools had superior resourcing and better results. Surely it was a no brainer to pay the money and get a better education.
With the benefit of hindsight I can say that I was very, very wrong for my family. There are clear reasons why private schools outperform public schools and though it has a little to do with teaching quality as they have more control over staffing processes, it is not the only factor. Despite odd employment practices in the public system, there are very fine, vocational teachers working in public schools working under demanding conditions.
The basic reason private schools outperform public schools in low SE schools is that cost of living clumps struggling families together. Many families in low SE areas lack the education to support their children, in many cases had poor experiences within the education system and subsequently lack support for the education system itself. The proportion of drug use, poor parental skills, unemployment, cultural issues, mental health issues, lack of tertiary study and lack of contact with their own children due to work commitments is much higher. The entry levels of students at low SE schools are much lower requiring more creative work by teachers in secondary school to access the curriculum. The skills of teachers in low SE schools is not just about curriculum, it's dealing with all the other issues too, whilst teaching children.
For most people, in higher SE areas there are few reasons not to use higher SE state schools, your decision should be based on local performance and perception. Investigate local issues with local parents to see what is really going on. Public documents will not reveal much. If parents talk about bullying and uncontrolled classes think about the local fee paying privates - but make sure it's not happening there too. Find out about the tenure of the Principal and their focus. Shifting students from public to private between primary and secondary is tempting but brings a considerable level of disruption to their learning whilst they adjust. There is risk in transition socially, emotionally and academically at a time of significant developmental change.
My own experience putting my first child in a high ranking independent private school from Kindergarten was not good. I was promised a thriving young girl and was delivered an unhappy child in a highly competitive environment, with little curriculum differentiation for a quirky student (as opposed to children at either end of the educational spectrum), poor pastoral care and a group of upwardly mobile people that we could not relate to. As the naive parent that initially proposed sending my child there, it is a decision I have forever regretted.
It's not that the school did not deliver for those parents that pressed their kids, wanted homework, were in the top 5% or had an ID, students that benefitted from strict curriculum delivery and desired upward mobility or were already wealthy and knew it. It just wasn't what we wanted for our kids. After four years of an unhappy child, we moved her to the local public school. It has taken two years for her to be a happy kid again and having normal developmental issues rather than social and curriculum ones. What I discovered was the difference of her being embedded with families of similar values outweighs perceived academic benefits. She could be a kid again and develop at her own pace together with our expectation that she would always give her best effort - not be coached beyond it through constant parental tutoring - the expectation at the private independent school to compete. If you are in a situation like us, I'd suggest rip off the band-aid and get them out, don't hesitate and don't struggle with the decision. It is the kindest thing to do for your child.
We all want the best for our kids. Mine can cope in an environment where they are instructed what to do and are happy to do it. At their new school there is little bullying and enough pastoral care available to deal with little issues. Teaching is a bit hit and miss as the environment is not particularly challenging and because there is no mechanism to weed teachers out if the teacher can't deliver.
We have three low fee private schools nearby and still have her enrolled at one in case of another parental catastrophic failure but I don't expect to use it. I know low fee paying private schools do pastoral care well and are less likely to do the "weed" out of students that do not fit purely the academic mould than the high performing Independent private schools. I have looked into the public feeder high school and am very happy with what I hear from parents at the primary school with older siblings, we should now be ok.
The low SES school that I taught at for so long has better teachers with a more diverse skill set. Students quickly identify the weak links in teaching staff and move them on. Kids that can't cope with the difficult environment move on to low fee private schools or higher SE public schools. Training of teachers is relentless to ensure best practices are maintained to prevent an unproductive environment. For kids struggling behaviourally it is a much better environment than a private school where they would be asked to leave and have their basic security challenged whilst they matured. For them the low SE public school is great as the school wants them and wants to help them mature.
For kids that grow up in the area, can survive the environment, are smart and get access to ATAR programs they wouldn't otherwise, they benefit from intense assistance (without these students the school would lack aspiration and growth). These kids are the pride of their schools, kids that do succeed, despite all the noise that interrupts their learning.
Given my obvious appreciation of low SE teachers, why did I not send my children there? My kids lack the social experiences to deal with the environment, I'll support them to university or whatever they choose, they do not need the extra support to cater to local requirements and don't have the skills to cope with the difficult students. Their home environment is not what I grew up in and they'll do better in a higher SES school.
I was a strong believer in the values education provided by a low fee private school, particularly the service beyond self ethos. I acknowledge when done well it is brilliant. I'm not so sure anymore that it is the norm though (after teaching briefly in one at the start of my career - it was superficial at best), but am open to considering it again - it's just that I've seen the service beyond self ethos in public schools provided by teachers in an authentic way, not forced by curriculum and wonder if this form to kids is more effective. Rotary Interact clubs are a great substitute for this with a win-win for the community and students, where students decide what they want to benefit and it's not a form of community service enforced slavery, tainting their perception of public service.
So, for me choosing a school, ultimately now is not about league tables - it's about cultural fit. Choose where your child will thrive and forget the rest - it will follow regardless. There will be exceptions, but the general rule is this - if it feels wrong it probably is. Ask some questions, make some changes and if it doesn't improve, if the child is not happy, move them. You are doing the right thing.