As a US person for tax purposes (including a citizen, green card holder, or non-green card holder who passes the substantial presence test) you are required to report and pay US tax on all your world-wide income.
The US provides either a deduction or a credit if you pay foreign income tax on the same income. You can choose the deduction or credit, whichever works best for you. Turbotax includes these forms and calculations.
You can read more here,
https://www.irs.gov/taxtopics/tc856
https://apps.irs.gov/app/vita/content/globalmedia/4491_foreign_tax_credit.pdf
https://www.irs.gov/individuals/international-taxpayers/foreign-tax-credit
https://www.irs.gov/forms-pubs/about-publication-514
https://www.irs.gov/individuals/international-taxpayers/foreign-taxes-that-qualify-for-the-foreign-t...
No one can tell you if it would be better to freelance for the German company without a deeper knowledge of German tax law, employment law, and your particular situation. In the US, being an employee carries certain benefits that do not apply to independent contractors. If that is the case with Germany, you would have to consider the tangible and intangible effect of those benefits. Your worldwide income would still be subject to US tax. If you didn't pay German income tax, you wouldn't claim the deduction or credit.
