It's impossible generalise. There are private schools and private schools. They are not automatically all better, academically or pastorally, than state schools. By going private all you really guarantee (generally) is smaller class sizes and more resources but that't the only constant.
Some private schools really prioritise excellence in all areas, in some basically you're just paying to be around a lot of posh kids.
It also depends hugely on your child and their personality, their academic ability, their peer group and where you live.
In some areas a private education is probably the only option for a good education. In others, many state schools are on par with or even better than the privates so you are literally pouring money down the drain.
If your child is very bright and motivated and has a similar peer group, private may be a complete waste of money. If your child has particular needs or is struggling in their peer group it may be the best money you've ever spent.
You really need to do some proper research into this and ask yourself what you really want from it. Are you doing it because academic excellence is really important to you? Or because your child is sensitive and struggles in larger, more anonymous environments? Or are you doing it because you want your child only to associate with certain other types of children?
This is a personal view and others might disagree but I think private primaries are largely a waste of money. At that age its about socialisation and pastoral care. All you're really doing by going private is guaranteeing they will only be around other fairly wealthy kids (which I personally wouldn't want but you might). At secondary level it becomes a better investment, based on where you are etc.