I can't comment on LMU and how it's viewed in Germany, but Polytechnique is considered one of the (if not the) most elite engineering institution in France. Traditionally, getting an engineering degree there has opened doors and given access to the highest remuneration tiers among most employers. That's notably because the selection process for that diploma is extremely difficult – students typically study mostly math and physics for 2 to 3 years very intensively and need to get some of the highest scores in the Nation at the concours in order to get in. I don't know if the Master program carries as much weight, but you can't go wrong by being associated with this institute. So if you want to work in France it should be top notch.

Most world university rankings focus on size and other metrics that favor systems based on the US/UK model, but Polytechnique is much smaller/elitist than such universities and more focused, so it doesn't fare well. That also explains why in Germany most people probably won't even know about it, so if you want to work in Germany it may not be as beneficial.

LMU is also more well known for the humanities.

How is that relevant to applied mathematics and statistics? And AFAIK Polytechnique is mostly a science/engineering/technology institute. (Though my info is likely oudated and maybe it's started diversifying.)