State of private pay
* Schools in the private sector are free to pay their employees whatever salaries they like. Some pay more than state schools, partly because they think this will attract more able teachers, but also because they may require different working hours and conditions, including Saturdays.
Sometimes there is the compensation of longer holiday breaks. Some schools may pay less and offer smaller classes and more motivated students as compensation. It's up to you to decide what package you value most.
As for pension arrangements, some private schools do pay into the Teachers'
Pension Scheme. This certainly helps transfers between the sectors.