You can look at the cost of living comparators, but here is a rough outline.
Starting salary in US for SDE is probably like 100k. Going of single income tax filings your approximate aggregate tax rate will be ~%15. if you have state income tax, prolly like ~20% aggregate.
In Germany you would start at something like $70k and get a 42% tax rate afaik.
So right there you get more than twice the money left over after taxes.
Living costs would probably be close to each other, rent is probably cheaper in Germany cities but groceries and goods are more expensive.
And health insurance and costs are a small percentage of the salary.
The only big difference is that in US you sort of need a car, but again, with monthly cost of a finance for a car you are still not hitting
The biggest difference in cost comes when you start having kids - in US you pay closer to 25% income for all things child related, so that eats into the extra money real quick. For outside of tech, if you make middle class salary in the 70k range, you are much better off in EU, because a lot of things are heavily subsidized.