I come from a mindset that people inhabiting my fantasy world want to survive. They know very well how their environment works, and they make decisions to the best of their ability within that environment that maximizes their chance of survival.
Ergo, if a commoner needs to take up arms to defend his home or his village, he will choose a weapon that maximizes his chance of surviving.
He will know whether swords or axes make the biggest wounds (he won't know d8 vs. d10, but he will know what kinds of wounds the weapons make).
He will know which weapon is harder to wield (he won't know he's -2 with a sword and -1 with an axe, but as soon as he's tried both implements, he will know which one he can use best).
Given that he will hit more often with an axe, and that the axe will make bigger wounds, he would see no reason at all to choose a sword.
He will maximize his chances of surviving by choosing an axe.
And, because axes are a dime a dozen in a medieval farm or village, and swords aren't, he won't likely be forced to choose an inferior sword because it's the only weapon lying around handy for him to find.
So yes, if the numbers we are discussing in this thread are true in 4e, then very nearly all of my commoners will be defending their homes with axes, not swords.