I am Aussie, lived in the UK for close to 15 years and had my children there, moved back to Australia 3 years ago, kids now 11 and 9.
We were in London and to be honest, gang crime was getting a bit too close to home, but obviously not all of the UK is like that, and we moved just outside a capital city here in Australia. Someone above mentioned drugs, but it isn't a big issue where I am here in Aus. Also, my oldest is July born and was always so far behind at school his first few years in the UK, he was just too young, he is flying at school now being in the right year level he should be in - but that is a reason personal to my family.
I would say home is where the heart, ie. family are. If you have family in the UK who you care about stay there. Moving with kids is hard, and a lot of people make their 'mum' friends when kids are babies, so if you move when they are bit older it is hard to make new friends...people are busy with their kids, partners, work, elderly parents, their existing friends...most people when you get a bit older do not seem to be looking for new friends.
Good points, schools are more chilled out, teachers don't seem as stressed as in the UK. Access to GP and medical services has been so good, there is often some cost involved, but I go to the most amazing bulk billing GP surgery. I have never been rushed out of a GP appointment. You just call up and get an appointment at a time convenient to you, it is amazing. The GP receptionists are nice, because they know you don't have to attend their surgery. My kids are loving living here and it is so much better for them than where we were in London. Being a teacher and a doctor, I really think you might be better off work/life balance wise.
I do know some expats who have got very homesick since covid, it is one thing living abroad when you think you can always just jump on a plane, but when you can't, it is very hard. I have an Indian friend who was so excited to start their new life in Australia, but was hopping back home a couple of times a year, now he can't do that because of covid he is thinking about moving back to India, primarily for family.
Lots to weigh up, I live in a lifestyle town and there are a lot of divorces, my theory is people move here to improve or fix things, but at the end of the day, a lot is same same but different, and your troubles can follow you.