Ax here, too. I mainly use axes against single opponents or when culling the herds or flocks on my farms. It's precise and does a lot of damage, especially on a crit. I only use swords vs. groups of opponents (zombies,) or if I have to attack quickly multiple times. I use bows vs. creepers, cave spiders, and ghasts.
Side effect is that my sword and bow tend to last a long time. I go through axes much faster.