Westbound I'd stick with SK, CPH is a nic airport to transfer into, and I like SK for daytime flights (nice catering, nice seats, friendly service, etc) and you can get into EWR/ORD/SEA non-stop on nice and new aircraft.
Eastbound is bound to be a night flight, and if I had a choice I would catch SQ JFK-FRA. Except for BA's New ClubWorld, which isn't *A, the best nighttime I've had has been in a SpaceBed. Also, if you can't sleep, I only have stellar experience with SQ service.
As for ruling out the others, my reasoning is that I have a servere distaste for LH, never tried NZ and have a couple very gruff experiences with UA (except asia based crews on intra-asia hauls). BD is out on grounds of cradle seats for eastbound. But I am considering NZ LHR-LAX for my next RTW just to try, as they have been getting good writing about the catering and service.
