The question is very good and valid. And the answers given are the correct ones but...

If you ask a Swiss person about the quality of the schools then you will find out which ones are good and which ones are not. Effectively if your children are going to the Gymnasium there is no problem they are all, more or less, good. The problem is that you need a good school before that to get them in. This is where local knowledge comes in.

Be aware though that you are likely to have to move to get the school of your choice as the norm is to go to the local school. If you send your children to an alternative there is likely to be a financial penalty ie you need to pay for the education. I know of someone who lived on the Aargau Zug border and half the town was in Zug the other in Aargau. The Zug part had a secondary school the Aargau lot needed to travel to Wohlen 15Km away instead of walking. They talked to the local director in Zug who said no problem send your kids to us. He never bothered to inform them about the 10K bill that they got 3 months later... They moved 1 km direction Zug and that was that.