BR over UA.
BR vs. NH. Tough one. I've done both, it's hard to tell someone to pick one over the other if its their first time on either.
I would chalk one up, as others are still saying, to BR. Great plane/layout. I find the lounges to be relatively the same (I'd give NH one point for the sake tastings). BR you get Rimowa amenity kit and there's "better" champagne.
What pushes BR over the edge is the way the total flight time is broken up you just have a relatively short flight to TPE and then on right away for the long haul to LAX. With going through Japan you have a 6-7h flight and then a 9-10h flight.