Thanks for the tip Jim!
Well, I had a phone call from my potentially new insurance agency and they let me off the hook. And my old agency called too and offered me a 15% discount. Now the monetary difference between the two offers is only 60 CHF, and often the old agency has a sharing fund program sort of like dividends, and passes them onto to their customers, which could mean I end up with no difference at all.
so all, in all, I learned a few things about contracts and have learned to be loyal to my current company, even if I am paying a bit more "on paper".
They, both companies, were very nice to understand that, well, I don't understand much.