How do different types of weapons compare? For example, is sword better than a mace, or are they different somehow?
There are two different types of attack, namely blunt and edged (sharp); In addition, each different weapon and material has different stats for Yield, Fracture and Elasticity, which are used to simulate proper Stress & Strain.
As this makes it impossible to give specifics, the general consensus is:
Notes: Copper is better at piercing Iron armor than Bronze is, but Bronze pierces Copper and Bronze armor and better than Copper does
Notes: All six non-adamantine metals perform nearly identically. Steel has a slightly higher rate of critical wounds, while silver is slightly more likely to penetrate armor.
Warhammers and Axes beat the pants offa Maces and Swords in their respective damage categories (i.e., edged vs. piercing)
Spears are off in their own little group.
Generally speaking, Axes do deadly deadly things to unarmored critters, Warhammers quickly cause crippling wounds (leaving enemies free to be maimed by the aforementioned axedwarves) and spears are useful against larger enemies such as megabeasts, forgotten beasts, and titans.
This thread might have the more detailed information you're interested in:
This came up in another question, but there is a long chart here:
I'd summarize it, but it boils down to: there aren't really any hard and fast rules on the issue.