But if the options include JAL or ANA, always take them over any US carrier. They are not even the same kind of thing compared to what we endure in the US.
You also have to consider safety (some airlines only fly Airbus planes, some are mostly Boeing), cost, and convenience.
BA on 777: really nice
Virgin Atlantic on A-340: awful
Icelandair on 757: truly awful
KLM on 777: pretty nice
I don't think just avoiding the American flag is enough.