Which course is most beneficial for someone working in a GS/GG position, Project Management Professional (PMP) or Lean Six Sigma?

So, if you are seeking one of these two certifications, be prepared to use them when putting them on your resume.
I have formal PMP training and decided not to put the cert on my resume after being a PM and later Program Manager. I found herding several different herds of cats to be boring and uninspiring. Just being a resource manager is more my cup of tea. But if you like relying upon others managing resources to accomplish many projects and you get all the disdain for the project slip and budget shortfall then by all means....
LSS is fine but its a stretch to apply it outside of manufacturing to any degree of success, IMO. We had them in FORSCOM HQ but all they did was collect GS-14 pay and produced nothing of consequence. After they touted their proposal, a new green suiter ACoS came in and pooh poohed the proposal and asked for another....wash, rinse, repeat...
I've had several arguments/discussions with LSS Green and Black belts. They have yet to convince me of their long-term practical use in the military (outside of fault reduction and QA/QC improvement in manufacturing and supply chain management).

Personally, I would rather have a person with the PMP. The LSS means you can look at manpower and processes - the PMP means you can get a tasking and use what you have to get the tasking done.

BUT - like I said, that's just my personal opinion.

The people I’ve worked with and spoken to prefer the PMP as it demonstrates experience and knowledge to plan, execute, monitor and closeout almost any type of project. The PMI methodology is geared to medium sized projects and not all applies to smaller projects, and may not be enough in itself for a billion dollar mega-project. If I remember correctly LSS is more narrowly focused and is geared towards improving process efficiency and serves as a good compliment to the PMP as LSS type of projects are looked at as specific type of project and as a good compliment to the PMP.

Also to maintain the PMP you need to meet the continuing certification requirements showing that you are maintaining your knowledge and skills. Some organizations that issue the LSS certification do not require any continuing education.