Airbus Instructors at Toulose insist on the usage of outboard armrest while pilots go there for training . I am referring to Fly by Airbus jetliners. It is part of the SOP for Airbus.
When it come to Boeing there is no right or wrong approach. I have seen cockpit videos of Boeing 787 dreamliner. The chief test pilot captain Mike Carricker flew the 787 with both armrests in up position.
Vast majority of Airlines pilots fly with both armrests down. . Armrests down results in very smotth and stable flying.
How ever if there is an emergency or a severe turbulence. It is best to fly with both armrests up .