Maces suck, quite frankly. So do axes. And bows.
The best weapons in the game are swords, spears, and magic-bolt-throwing staves. The reasoning:
Swords:
Swords often give a bonus to initiative, which is a huge thing in this game. being able to take more turns than your enemy, essentially equates to a massive amount of extra damage due to attacking more often, and it more than makes up for the relatively lower damage. Counterattacks are also amazing, they simply compound the above. A counterattack is essentially ANOTHER free turn, although one in which you don't get to choose what you do. What it means is that someone with a longsword can do 2-3x the overall damage compared to a mace user, simply due to hitting more often.
Swords combine amazingly with shields. you can advance on the enemy and defend infront of them with your shield up, resuting in you taking far less damage from an incoming attack, and then getting a free counterattack against the enemy, who is NOT in a defensive stance. The athican longsword with it's two counterattacks is just overkill. Personally i think, to balance swords, the counterattack should either not be reliable (50% chance to trigger?), or counterattacking should delay your next turn by giving a temporary penalty to initiative. also lower the damage of all sword weapons.
Axes:
Axes sometimes have an initiative penalty, and we've already established that sucks. The backswing ability is kind of neat, but the AI doesn't use evasion enough for you to need it. and it doesn't compare to counterattacking. an axe is basically just an inferior sword, and they only have real usefulness against warg riders. Axes need more damage, more initiative, and perhaps counterattacks of their own. An ability to destroy shields might be fun too
Spears:
Spears have armour penetration, which is very useful in the lategame against plate armour. The immunity to counterattacks also makes them a good counter to swords. However, i feel that their damage just isn't high enough, and unless you're playing krax, the inability to use a shield with one kind of cripples you defensively. Given the long reach of a spear, i feel that spear type weapons should have an inherent initiative bonus (more than swords) or that they should be able to attack over a distance of 2 tiles, instead of 1. bonuses versus mounted units would be nice too, as the game has almost no incentive not to stick each and every soldier on a horse, as is.
Maces:
Maces suck. The initiative penalty pretty much kills them, regardless of anything else. They do tend to have the highest base damage, but this doesn't matter much - spears are better and often hit harder, due to the armor penetration. Lategame is even worse, as plate armour has double defense against blunt weapons, which just drives another nail into the coffin.
The Bash ability is a nice idea in theory, but in practical terms it isn't very useful. Unless you're already overwhelmingly more powerful, the chance of it proccing is simply too low to be reliable, and if you ARE that powerful then you don't need to stun anyone, you're probably killing them in one hit anyway. And as others have pointed out, being able to deny your enemy an occasional turn is pretty much negated by the initiative penalty giving YOU less turns, too. The only time that maces can really be useful is if you're teaming up against some huge target, such as a dragon. Get several people with hammers pounding on it, and you might be able to stunlock it into eternity, but that's assuming you don't get fireballed to death as the dragon takes three free turns at the start of the battle first.
I do have a simple suggestion to make maces better. Take away the Bash ability, and give them splash damage instead - dealing 50% of the attack's damage to all enemies within 1 tile of the target. This would give maces a purpose, a niche to fill, as crowd control.
Bows:
Bows suck. They do. The main reason is their low damage. Although a bow can be useful earlygame against bandits and darklings, all it takes is a suit of leather armour and a wooden shield to make bows virtually worthless. it feels like they're affected more strongly by defense, than other types of weapons. The tarth do have a bow with armour penetration, but it's right at the far end of the tech tree, which i feel is pointless. I think ALL bows need some amount of armor penetration if they're to be of much use at all, and less of an initiative penalty
Magic staffs:
The best troop weapon in the game by far. The ember/frost staff at 6 damage, and later the upgraded versions which do 13 damage iirc. These staves fire magical bolts of energy, and so they are ranged weapons. However, they are very difficult to resist, as they ignore both "defense" and "magic resist" entirely, dealing their full damage unless the target specifically resists that element.
In all practical terms, they fill the same role as bows, they have the initiative penalty, and you shoot them from afar, and they have roughly equivilant damage. But magic staffs are like bows if they all had 100% armour penetration. They're miles better and there's just no comparison. Magic staves need nerfing badly. The easiest way i can see, is to make Magic Resist reduce the damage from them, in addition to elemental resistance. Having a bigger initiative penalty on them compared to bows would help to balance them, too
IMO, you can steamroll any army in the game using ice staves and athican longswords, alongside some half decent armour on the sword troops. Two troop archetypes are all you need to dominate the world, even the spears are optional. The weapon types are not balanced at all, imo. to that end, i'd also say the kingdom of altar is overpowered, as they have the best unique variant of the best kind of weapon. And don't even get me started on henchmen stacking auras.....