It's not different for managers. An L6 manager at Amazon for example will make around USD$170k total comp in Munich while new Seattle offers sit at $380k or more.
You will take at least a 55% pay cut -- and that's just pre-tax. Now consider Germany's 44% effective tax rate versus Seattle's 32% effective tax rate. The chasm gets even wider.
You get the double hit of massively reduced salaries and massive increased taxes.
How about purchasing power? Even more bad news. Local purchasing power in Munich is 40% lower than Seattle. Yet another hit.
Don't forget Germany recently also hiked their sales tax to 19%(!!!), which is almost double Seattle.
The higher you get on the seniority ladder, the worse the comparisons get. You can't get the equivalent of US$500k without being an executive, or for extreme outliers. US$500k is garden variety staff level in most top tier US companies.
Work just as hard as your US counterparts for a MASSIVELY reduced rate. Over 10 years, you've lost literally millions of dollars.