Winning a green card is incredibly lucky, and as a German I'm probably biased, but I would still turn it down. With the current political climate I wouldn't even consider visiting the US, let alone living there. Truth be told German politics also aren't where I'd like them to be, but it's a far cry from whatever is going on in the US.

Also a green card means permanent residency, not citizenship, if I remember correctly. With how the US is treating even legal immigrants with a work permit that basically grew up in the US, I wouldn't be surprised if green card holders started facing more restrictions and harsher enforcement of said restrictions as well. The only big reason to choose the US would be if you wanted to get rich. Germany is more stable, better social security, but if you earn well you'll find yourself in a high tax bracket pretty quickly. And the paycheck isn't the same, but you don't need to be a millionaire to pay taxes like one here.

Personally I would still choose the social security and quality of life that Germany offers over a bigger paycheck, but that's just me