Your assets are your assets in every other first world country. US, UK, EU all have segregation requirements for customer assets. CH is not unique here.
(Also, if by “your assets” you mean that you would be the shareholder on CSD records, sorry to disappoint but no, that’s not the case in switzerland, your securities are held “in the street name” here too. This actually depends more on the CSD you’re dealing with than the broker and broker’s country. SIX SIS is a street name CSD)
The main thing that can go wrong is broker fraud: what happens if at the time of bankruptcy, the broker actually carried less shares (according to central depositories’ books) than what it told its customers? That’s why you stick with well established, highly respected names like IBKR. And not some fly by night operations. Actual chance of broker bankruptcy if they are sticking strictly to brokering, commissions cover their operating expenses, and they are not doing anything shady on the side (prop trading etc) is very small. Brokering is very low risk activity.
100k esisuisse coverage only applies to cash balances, not securities. So, pretty much irrelevant unless you use your swissquote account for banking rather than investing
IMHO, IBKR is much safer choice. The reason is pretty simple - follow the (smart) money. Swissquote from what I could find, with difficulties, has maybe $25B AUM, IBKR - $237B. Huge number of professional investors and smaller hedge funds use them. If they ever have a fraud problem, you’d be in a very good company. They’re subject to US security regulations, one of the best / most well known in the world, unlike swissquote who are just a regional player