Ka6crpe, Two things:
Who has got the money is an important consideration but MORE important is who's flight you are booked on. If it is a LHnnnn flight number then the marketing carrier is LH regardless of who actually operates the flight. I believe NZ code-shares on that flight ...
Trans-atlantic flights rarely use the shortest GCM path. Winds over the Atlantic, and in particular the jet stream have a big influence on the track your particular flight takes. You may get lucky and have a more northerly routing and you will see Greenland (spectacular) and the iceberg filled waters ... On the other hand you may get a southerly routing and miss a lot of the white stuff.
It's not possible to know in advance what the winds will be doing on the day of your flight, but good luck.