In my experience, private schools do not necessarily have higher salary than state schools, particularly at management levels; lots are coming out of the TPS which is a major benefit for teachers; and there certainly is NOT more money to be spent on teaching resources. For many private schools, staffing is by far their biggest cost. Once grounds are maintained there is little left for educational resources.
There is some exceptionally good teaching going on in the state sector, which tends to be more research informed. Some teaching (not all, of course) in private schools is woeful but there is less monitoring of staff- which can be a bonus for teachers- but means poor practice is not always weeded out.
Yes- classes are smaller and holidays are longer. But the average day is longer and teachers are expected to do more duties and after-school activities and attend more events outside school hours, so that evens up in the end.
On the whole behaviour is better as there tend not to be extremes of poor behaviour. However, it is certainly not the case in my experience that the children are all well-motivated students with supportive parents. Levels of apathy are high and many parents now think they have signed the cheque so it is all the responsibility of the school. Parents want the children to do well but they don't want them to have to work hard- they want the teachers to work hard and the children to have a lovely time.
SEND support is also a massive issue. We have increasing numbers of children with SEND with varying needs but compared to many state schools, we do not have the resources or expertise to support them adequately (which is saying something given the pressures the state sector is facing).
So still some benefits to working in the private sector, but increasingly in my experience, the benefits are being eroded and a good state school is an attractive proposition that often pays better.