It depends. Both products are very similar, but there are still some differences:

Seats: The LX seat is closer to the aisle, smaller armrest there. But it has a privacy screen and a wider armrest in the middle. So more likely to be disturbed by people walking by, but more privacy from you seatmate. LX has the ottoman, LH a folding footrest. Also LX has only 1-2-1, i dislike the 2-2 config in the 747 when traveling alone. LX also 'makes' you bed, on LH you just have a blanket and pillow. Never been in the new LX F.

Amenity Kit and PJ: No PJ on day flights on LH, both kits are nothing to write home (but the current LH Rimowa Kit fetches up to 80 Euro on Ebay).

Food: No caviar on LX. Otherwise similar, depending more on the catering station.

Service: very dependend on crew. I find the LH MUC crews better than the FRA crews, LX usually very good, but i had grumpy LX crews before.

Lounge: Don't like the ZRH setup too much. Lounge is outside of security, for US flights they drive you to the E terminal, but you need to go thru security twice. And they dump you there much too long before the flight.

For me: LH thru MUC is first choice, then LX via ZRH and LH via FRA is last.