Former teacher. Just wanted to give some perspective on what's been discussed recently.

Private sector/tuition can be very liberating. Much more autonomy to teach what you think best, etc. I don't think the private education sector is in particularly great shape at the moment, though. There's quite a big risk. I know of a DD at MOE who left for private sector and the company closed less than 6 months later. Heard of tuition centres poaching tutors to get their students to enroll. If the system is cannibalizing itself, maybe it's not the best time to join.

Re independent schools, it's good if you find yourself aligned with values of the school. Downside is that upward progression can be more difficult. In MOE, if it's time for you to become HOD/VP, there's almost always a school SOMEWHERE that needs a new HOD/VP. In an independent school, opportunities are based on attrition, essentially.