You're correct! Axes do not do as much damage as they do in Vanilla Minecraft in SkyWars. This is because when 1.9 was initially released, Axes were a lot more powerful than they used to be. Due to the fact that axes outputted such large volumes of with the initial hit, it meant that people were using an Axe to land an initial hit on a player, then swapping to a sword. It meant that as a player being leaped on you had very little chance to defend yourself as the initial hit was so strong. This meant with the initial release on 1.9, we nerfed damage of Axes based on feedback at the time.
Now time has passed since then I'm more willing to up the damage output again if other people support the increase of damage of Axes in SkyWars.