• BA will have non-stop flights. If you book LH, then you'll inevitable have to fly through Frankfurt or Munich
• Check the aircraft types that will operate the route on your dates. I've looked at random dates in April: LH operates an A350 to Munich and the 747-400 to Frankfurt. BA operates an A350. The 747 are obviously older and noisier than the more recent A350.

If you are flying in business class, then I would probably prefer BA over LH (unless BA was substantially more expensive than the other options)as the seat in their A350 is much better than LH's current seat. Even AC's seat would be better than LH.