My parents went abroad when I was nearly 13, and my sister and I went to a new school with an entirely different curriculum and lots of nationalities. I stayed there until 18 and loved it.
My aunt and uncle moved around every four years and their children went to boarding school in the UK. It suited two of the children, but one of them - a much more sensitive soul - probably would have been better off with his parents.
My sister is now in a similar position to yours - she and her husband move countries every 2.5 years on average. She has decided to keep her children in IB schools, so at least when they change country there is continuity of curriculum. Basically her choice was between the French sytem (her husband is French) or the IB system, and she went for the IB system. Having said that, she's not overly excited by the quality of the schools she's seen, despite the horribly high fees, and there is an awful lot of turnover in the school population, which is very disruptive. Her children are happy so far, though - they are, fortunately, extremely bright and outgoing.
I live in Paris and I'm going to send my daughter to a French-English bilingual school.
Basically you need to consider that children must have some kind of continuity in their lives at school - the continuity of the parental home is not enough/sufficient. If there is going to be a lot of disruption at school (different language/curriculum/quality of education), you should probably look at boarding school. Otherwise, you can probably keep the children with you.