I think you have answered your own question.

Put them in the local school, they will learn the language, have local friends and integrate into the community.

Put them into an Internations school will keep them as an outsider. Plus cost you a small fortune.

We have just decided to out our son into Kindergarten, even though

1/ This means paying the full-time nursery/kindercrippe costs for 2 more years as Kindergarten is not full time

2/ We would have a free place in the international system.