What this comparison does
Comparing two salaries across a border by converting one at the exchange rate answers the wrong question. It tells you what your money would be worth if you spent it in the country you left. What you want to know is what it buys where you would actually live, after that country's tax system has taken its share.
These pages do it in three steps. First, the salary you enter is converted into the salary that buys the same basket in the other place, using official purchasing power parities. Second, both salaries go through the withholding rules of their own jurisdiction for the tax year shown on the page. Third, the resulting net pay is brought back to one set of prices so the two figures can be read against each other. The difference that remains is the difference between the two tax systems.
Real take-home
The row labelled real take-home is the one to read. It is each side's net pay expressed at the origin's price level. Net pay on its own is not comparable across a border: two figures in two currencies at two price levels have no common scale. The nominal figures stay on the page next to it, because a number that has been adjusted should always be shown beside the number it was adjusted from.
What the defaults assume
Each side is calculated with the default options its own jurisdiction declares, and those options are listed under each column. That normally means a single filer with no dependants and no optional deductions. There is no shared marital status control, and that is deliberate: mapping one setting onto two countries' filing concepts would be a guess about tax law, and the German tax class that looks like "married" assumes a spouse in another class with no income of their own. To change any of it, follow the link to that place's own salary page.
The limits worth knowing
Withholding is not a tax return. It ignores deductible expenses, other income and credits that arrive at assessment. Price levels are published a year or two behind tax rules, so the two years on the page are usually different; both are stated rather than blended. And a national price level says nothing about the city you would move to or the rent you would sign.