If you plan on staying in Switzerland long-term, I suggest taking into consideration putting your kids into the local system. If you're worried about the language, don't , my father spoke English to me and my mom Chinese, and I first learned Italian (the local language in Ticino) in kindergarten. I did all my schooling till highschool in Italian, but English has always been the language I think in and the language I'm most comfortable with (in fact, I speak Italian fluently, but I don't write very well because I tend to write with an "English" structure...I suppose because I read a lot as a kid, but always in English).
So I'd like to give you my perspective, from the "other" side, as a "kid" (I'm studying mechanical engineering now at ETH Zurich) who did the Swiss system, but saw what it was like in the international system (my brother and cousins went to international schools).
At a highschool level, I found the Swiss system to be quite good and give a very solid foundation, although sometimes they have a somewhat....archaic way of teaching ("traditional" they would say ^__~) and are not very flexible. I remember my brother doing a lot of subjects that were similar to mine, but more interactive and dynamic, for example in philosophy class I had to study texts by plato etc. and interpret them, whereas my brother would give presentations for his ToK (Theory of Knowledge) class, where he would have to analyze a current event for it's social and philosophical implications.
However, in a lot of subjects they were rather behind and classes weren't as serious, particularly math and sciences: my brother's math classes seemed to have more "why math is important in life" than actual math, and I remember in one test, students would receive points for making an "original drawing of a problem-solving process", which quite frankly is somewhat ridiculous... (I would agree with a point for drawing the concept correctly, but the teacher was actually giving points based on how "original" and nice the drawing was...)
The teachers also pay a lot more attention to the individual kid, which is a double-edged sword. The advantage is of course kids get more help and guidance, the big disadvantage is that they tend to get used to not being independent. By the time I was in highschool, I studied because I wanted to study; I stopped showing my parents my grades (in fact, they were really surprised that I almost failed one year), and started just studying more when I saw I needed to, whereas my brother and most of his friends (from what I saw) did their homework because they had someone watching over their shoulder. The problem is that a lot of these kids lack self-discipline once they get to university, and very often aren't really sure what they even want to do since they've never thought about it. This is imho the biggest disadvantage of international schools (similar to the problem of home-schooling).