One downside of getting US citizenship is that if you later move to another country (your original country or a third country), you will obligated to continue to file US income tax returns, and potentially pay US income taxes. Depending on your circumstances, your tax filing might be trivial or it might be complicated, and you may or may not actually owe taxes to the US. So this might be a minor annual hassle, or it might be a painful, time consuming and expensive process. It is possible to later give up your US citizenship, but it takes time and costs money.

That's it so far as I know. If you are, for example, a Japanese or German national then naturalizing as a US citizen may be an issue for your current citizenship. (Germany will likely grant you permission to naturalize; Japan will not.)

If you are already a green card holder, you are already subject to the tax and other reporting requirements like a US citizen so the only real difference from the US perspective is you can't vote and aren't guaranteed to be able to cross the US border. It's that last bit that most people really want.

The US has tax on all income regardless of residency.