It is certainly possible and highly likely that the family office benefits from institutional pricing, which is generally much more favorable than pricing for private individuals. So it could easily offer you lower pricing for the same product.
The question to ask yourself is whether you need the services provided by the family office. Do you need concierge services, legal services, property management, etc? If all you need is asset management, then you can comfortably avoid the family office fees. You can also radically reduce your asset management costs by moving to a more affordable Swiss asset management service.
You certainly can find better than 1.1% per annum. That is especially true if the 1.1% is the asset management fee and fund costs (TERs) are deducted on top of that. Swiss banks now have Internet-based asset management services with flat fees as low as 0.75% plus 0.25% fund costs (PostFinance) or 0.45% plus 0.5% fund costs (Swissquote, with more than 350,000 francs of assets). Swiss non-bank asset management services like True Wealth charge as little as 0.5% in total (including fund costs), depending on how many assets you hold with them.
You can use the asset management comparison right here on moneyland.ch to get a good idea of how much you could save.
These low-cost Swiss asset management services generally use passive management, and invest mainly in passive ETFs and index funds. If you have been using a Swiss private bank which actively seeks out and invests in specialized investments, there is a chance that returns may be slightly lower (or not). Otherwise, passive investing generally bears less risk than active investing.
As far as risks with regards to family offices are concerned: Using a family office often requires making the family office a trustee or giving power of attorney over your bank accounts and investments. You will want to make sure that this third party is reputable and reliable before granting it that kind of power.
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