My DH works in a private school and doesn't like it. It is a mixed sex school which used to be a boys' school. It's often the girls he says he doesn't like though!
He mainly doesn't like the same things a teacher in state might say : lots of initiatives, learning walks for form time/ spying through doors and declining behaviour standards. He used to work in a state school in a deprived area and was happier : that said, that was years ago and I reckon he'd get a big shock if he returned to the state sector.
He doesn't like his SLT who can be bullies (no time off allowed for anything, for example) but they can be like that anywhere!
His school probably ahs better staff cohesion than mime : papers and a telly in the staffroom, staff socials. \He used to go out a fair amount with staff, although he does this far less. I can't decide if this is him being older or whether the school ahs changed. Both, I think.
The grass is not always greener on the other side. He really ahs very little support or equipment (I have a laptop for example; he gets nothing) and the buildings and classrooms he works in are run down, as are mine but I expect it!
An ex colleague of mine went to work in an all girls school and is very happy despite a longer commute - mainly because she has more autonomy and no more difficult boys. She does comment on her marking, though. There is an expectation of thorough marking and girls write a lot!
Don't forget private schools often expect a commitment to extra curricular .
I think some of it may depend on the subject you teach : DH is a maths teacher so doesn't want to be particularly creative or autonomous,; friend is an English teacher so is enjoying the opportunity to take longer over teaching texts and be more creative.
In general, class sizes are smaller , but DH does have classes of 28. Any state school 'initiative' does tend to reach his school, with maybe a two year time lag. He has longer holidays : but he gets bored! he's really easy to live with
Go and visit the school ; you'll get a good sense of it from doing so.
I have been for interviews twice in all girls' schools and withdrew each time : I found them too staid for me. I also couldn't really buy into the smug ethos which I sensed . I would say you have to buy into the concept of private education to feel comfortable in one.