Taught in both (primary age) and had DCs in both. It really does depend on your local options. I was amazed in one private school how many parents paid to send their children to our school despite living in catchments areas of utterly amazing state village primary schools where the nature of the area and class sizes means it is so similar to a prep school. This makes no sense. Likewise we sent our own to prep school after a move as all the local options were pretty rubbish. After a few terms it became clear that our children didn't warrant much attention in their classes of 30 as they weren't on EHCPs or IEPs. The teacher of one of mine calling them by the wrong name (and clearly having mixed them up with another boy) was the final straw for me. I don't begrudge the staff that, they have too many to look after. In a prep school the teacher will know the pupils very very well in my experience - and that will carry on as they move through the school meaning a very personalised, nurturing time for their whole time there.
What I would say is if your child is pretty "middling" they will probably do better in a private school - in big classes in state schools teachers often know their brightest (those they have to set extra work for) and those who need most support / behavioural help best rather than those who are in the middle and just get on. The enrichment experiences, after school clubs etc are much much better in all prep schools I've been to and taught in. It is an expectation that teachers, and often TAs, provide a club as well as more experienced sports coaches etc offering football, rugby etc.
Another thing to remember is there are different levels of private school. The first I worked in was very rough and ready - no marketing team, posh facilities etc, the second much more middle ground. We visited one for our children that was way too posh for our liking , and of course much more expensive! I would say these higher end ones are really a waste of money, unless you a a multi millionaire where it is no issue to you at all. I think the middle one was probably the best, it gave better opportunities (amazing school productions, music lessons and shows, better libraries and ICT equipment, trips, clubs etc) so you felt you were getting more for paying for education which could be free in a state school - you felt the benefit more. In the first - "rough and ready" it felt very much it was just offering what a good state school should because those in the local area were not really up to scratch.
Also don't forget to take into account the extra costs that aren't part of school fees - can you "keep up with the Jones'" as it were? While this may not be important to you (quite rightly) it likely will become an issue with your little ones when they reach the higher end of prep age or senior school age and they can't have the latest tech, labels and experiences their friend do! This can be a real consideration. Can you afford the £1,000 school ski trip all their mates are going on, the £50 blazer for their uniform, the social events etc. Even within private schools you will have those who are struggling like mad to pay the fees and those who aren't bothered by it one bit.
In short - is private worth it? It depends wholly on what options you have around you. I know parents who have paid for private prep schools (which are cheaper than private senior schools) as a sort of long term private tutoring to get their DC to pas the 11+ and into grammar schools. If you have good local schools, especially if the fees will cause you to adjust your lifestyle and make too many sacrifices then no it isn't. If your children love things like music, drama and so on, especially at Prep age, private can bring a lot of advantages and opportunities state may not provide.