Here is my take. Now, we moved here a few months ago, kids are 8 and 5, and we are all at the beginning stages of learning German. We considered local schools, international schools, and the local Montessori school. We picked Montessori for a few reasons:
1. We were in a Montessori in the US because of this exact situation, we knew one day we would be moving, probably internationally. Montessori schools teach the same thing all over the world. My kids walked into school the first day and knew where they were and got to work. I was nervous about putting them in the local school because Montessori is different than other methods and I didn't want them to have to learn a different way to learn, and a new language and a new country at the same time. Also, I didn't have experience with the local school here and was told it can be a hit or miss depending on the canton and school itself. If we knew the teachers and the kids and the teaching method we may have chosen local. Also, the future doesn't tell us if we will be here for 4 years or 14, so keeping the same learning method would be good for moving somewhere else...
2. We want them to learn German and Swiss German. The Montessori School teaches in High German, the local kids speak Swiss. The International Schools teach in English with 'German as a second language' and we wanted them to learn it like a younger kid can, in their daily life.
3. The students at the Mont school are mostly local, with some international. I love that they hang out with local kids and learn how the lives of the Swiss are different than the US. They start English (and French) classes in Kindergarten (twice a week!) and by 2nd grade are able to communicate effectively so my kids didn't feel left out. They love practicing their English with a native speaker.
4. The Mont school is too far to walk but we have a short train ride and walk. My 8 yr old could do it on her own but my 5 yr old is still too spacey to cross the big street in front of the train station. We definitely wanted a school close to public transit, preferably the train.
5. Most of the teachers at the Mont School speak English quite well so I can speak freely with them about the kids. They teach my kids in English (temporarily) transitioning them to High German, and after 3 weeks in school I am starting to see a glimmer of understanding of German. The 5 yr old also has a special German language class once a week with 2 other young international classmates mostly because the kids in Kindergarten don't speak much English yet. It gives them a jumpstart to understanding what is going on. The 5 yr old will be learning to read/write in English in early elementary age, which I though I would have to do myself. Whew!
6. We have the choice of two (main) international schools here, one is huge and one is small. The itty bitty school was wonderful and we seriously considered it, but they teach in English, so we said no. The huge one was too big for us, right off the bat. And I wasn't impressed with the behavior of the kids. All speaking English is fine but they are rude and loud on the train, and seem to favor curse words whenever possible (of course, that could be true @ swiss kids, I just don't understand what they are saying, yet!). The large one offered a community of English speaking families (I call it the International School bubble) that you could probably camp yourself in for years and never experience Switzerland with the Swiss. No judgement here for those who choose that, it just wasn't for me. I didn't want the opportunity to be part of the bubble, too tempting! The Mont School community isn't very active like most US schools, but the families there are wonderful and helpful. That is also true of the public schools, although my teacher friend says there are 'PTA' type groups starting to form here in some schools.
The schooling here vs the US is definitely different, but both have their positives and not so positives... I spoke to a family who has been here several years, their daughter grew up here so knows the languages, loved preschool and public Kindergarten, but by 1st grade they were unhappy because the school wasn't rigorous enough by US standards, and she was bored. So they moved her to a private (not Montessori) school. This can be an issue in the US as well, so it isn't just Swiss. Another (native) family took their kids out of public school because some older teachers insisted on teaching in Swiss German to their students and wouldn't teach in High German. But on the flip side, I am friends with a teacher at the local public school and know parents who use them and are very happy.
I think it boils down to your expectations for the school. Rigorous curriculum? Language (English and/or German) immersion? Curriculum that is transferrable to another country, or even to another canton? And do you feel comfortable at the school? What type of school community are you looking for? Does location/public transit matter? We sold our house when we came here, expecting that we may want to stay long term. If we knew we were staying for only a few years our choice would probably have been the same.
This post was longer than I expected it to be! I hope it gives you different points to consider. We are happy with our choice, but each family has different needs and lives. Good luck to you!