Do the different weapon types have hidden properties in Loop Hero?

I noticed that the Axe consistently has higher base damage than other weapons (except at level 1 where every weapon has a base damage of 4-6), but I'm wondering if there's a "hidden cost" of using that weapon type such as lower attack speed or lower accuracy? Otherwise I'm wondering why would I choose to use, say a Lance that seems to have lower damage than weapons of a similar level. (Unless I get a level 4 Lance while my current weapon is level 2 or something like that, of course)

Thanks