I also agree that the showers are nearly equivalent. The UA showers have had a cool terrycloth bathrobe with a UA logo. That's about the only difference. And yes, temperature varies quite a bit. Perhaps the jolt of cold is a jet lag helper?

The factors I would consider if I were you:

1. Time. If the showers are booked at UA, head for the main Senator LH lounge (is is on the C concourse?) on the one closest to your connection. You might not be competing with as many people arriving at that time on LH. The larger LH Senator lounges definitely have more showers that UA. Don't begrudge the walk over to one of the Sen lounges. You are going to have to make it anyway for your CDG connection. Why not do the long walk through the corridors out of the way early?

2. Food and amenities. If time seems to be on your side, do the UA lounge with the Arrivals routine. The F class UA lounge is better in some people's opinion than the best that the Sen LH lounges can offer, although the food that LH offers is superior to what the RCC sets out to the non-F class folks.