As a middle-class American who lived and worked for a decade in Switzerland (and I made more money there), I can confirm that I always paid less as a percentage in Switzerland.
The problem is that the US tax system is so complex that once you reach a certain level of wealth, it pays for you to have someone find those loopholes. Warren Buffet famously decried that he pays lower taxes than his secretary, for example: http://money.cnn.com/2013/03/04/news/economy/buffett-secreta...
Swiss roads have no potholes, there are no homeless, they have universal healthcare and a free university system. I've lived there and I paid less in taxes, and one big difference is that the wealthy pony up their fair share.
wealthy pay, superwealthy just a bit due to special tax deals (which still benefits the country compared to them leaving for say Monaco or gazillion of other tax havens all around the globe).