What is more valuable in the civilian workforce, 6 Sigma Green Belt or PMP certification?

Both are good. PMP is more common but you should be good with either. The trick with LSS is that you need the formal certification not just a certificate stating you attended a class. The Military has a habit of putting folks through the class but they don't have the certification.

I have both and PMP will open more doors. LSS I'd good but there are so many groups that certify it's hard to know if your cert is worth it.

I recommend PMP over GreenBelt LSS. PMP is the most common certification for any government position. For many government positions they want PMP and Agile SAFE certifications. If you are going to do LSS then you will need to target the Black Belt and focus on Lean processes in manufacturing, process engineering. The Six Sigma part is all about being able to map processes in different methods and models.
The link for Agile SAFE is below.
https://www.scaledagileframework.com/