Highly likely southern route because ANA has been operating NH 237/238 (NRT-BRU) via non-stop southern route as cargo only flights since this situation has started. (i.e. NRT-BRU is a vaccination express). ANA said in average the flight 237/238 is taking 3 hrs. and 30 min, longer than over Russia route.

ANA 237 March 4

JAL has said they have experience of flying polar route from back in the days of NRT-ANC-Europe days of 1992 and before, because of that know how JAL said they chose polar route. ANA said they do not have experience of polar route, especially polar region between Alaska and Europe there is no alternate airport, hence ANA said they chose southern route.

There are many factors which influence flight path, not just the distance. Another factor is jet stream, can see on this world jet stream map (place the map to show Europe on left end and Japan on right end). Jet stream flow from west to east on the exact same path as southern Japan - Europe route. Flying from Europe to Japan maybe great but flying east to west on Japan - Europe route is facing jet stream face on most of the time. But flying polar route can avoid jet stream on many parts, which does influence fuel consumption and flight time. Some has experience flying NRT-SIN during winter time is about 7 hrs, plus, but reverse route of SIN-NRT during winter time can be short 5 hrs. plus, this is due to jet stream.

Another is atmospheric temperature, even at 40,000 ft. temperature is different from polar region and south Asian area. Cold air is denser than warmer air, which cold air provide more lift than warm air. You may have noticed that aircraft use less runway distance to take off at Anchorage than Honolulu, which is true. Many airlines flying India - Europe/Far East Aisa tend to schedule departure from India in late evening has this reason behind.

One more thing is fees airlines pay flying over any countries. Flying polar route is international water, which airlines does not have to pay any overflight fees, where southern route fly over multiple countries, which does add overflight fees an airline has to pay.

There are multiple factors influence when choosing a route, not just the distance. ANA and JAL have different experience/expertise, company personnel locations around the world to assist the flight has influence. However, currently passenger load is very light, which aircraft can fly longer distance with full load of fuel. It is possible that if the passenger load is like pre-pandemic then the situation can be different.