A matter of perspective and Ax versus Sword
What I find interesting is that if we had Vikings armed with modern weaponry raiding our country in 2014 we would all be far less admiring of their martial ability and motivations.
As far as the use of the ax versus the sword, the ax and ax-like weapons never lost effectiveness as a primary weapon even during the early years of the gunpowder age. The same cannot be said of the sword. Less than three hundred years from the time this series is set, the Saxons would nearly defeat the invading Normans (descendants of Vikings living in northern France) using large two handed axes. The Saxons defeat very nearly did not happen. Perhaps if they had not been fatigued by the long and fast march south after defeating another invading Scandinavian army in the North; they would have maintained better discipline and not have broken their shield wall in pursuit of a Norman feigned retreat. That break from their defensive formation cost the Saxons the battle and ultimately their country. The Normans are presumed to have had the superior weapons and weapon systems, but they still nearly lost to a small core of ax armed professional soldiers supported by variously armed militia.