Second of all, the greataxe is useless. Look at it. 1d12. The maul and greatsword (which are otherwise similar to the greataxe) have 2d6. Just think about that for a second. The greataxe can deal 1-12 damage. The maul can deal 2-12 damage. In fact, if you do the math, 2d6 averages one point higher than 1d12. So why in the world would anyone use the greataxe?
It crits better. The average (which for normal damage is 0.5 points apart) comes out pretty much the same, depending a little bit on how often you hit.
I agree that there are problems with the weapon list. It's filled with dud weapons; system mastery rears its head again. I was really hoping they'd fix these before final release. As shown (not considering external effects like limited weapon proficiencies driving particular choices, class features or feats improving certain weapons, magic weapon choices, etc.), and not considering cost and weight as important factors since they're all pretty low:
- The club, the greatclub, and the mace(!), are strictly inferior to the quarterstaff. The only thing granting even the quarterstaff some value is that it's the only decent bludgeoning simple weapon.
- Why does the light hammer do less damage than the handaxe?
The only simple melee weapons worth considering are the dagger (for finesse), the handaxe, the javelin (maybe, for throwing range, although a spear is better otherwise), the quarterstaff (if you really want bludgeoning damage), and the spear. The rest are traps.
Similarly, the morningstar is only useful if you want a piercing weapon and really don't care about using Dex with it (otherwise use a rapier), and the trident is just a more expensive, heavier spear. Why is the trident a martial weapon? Why does it even exist as separate from a spear?