Well, personal taste plays a factor (especially in Adventurer).
As far as the wiki is concerned (
Link-tastic), most weapons deal somewhat similar levels of damage, though exactly what they damage seems to vary.
Bludgeoning weapons cause more external damage, and don't get stuck.
Slashing weapons can hack off limbs (which is always awesome), but may get stuck.
Piercing weapons cause more internal wounds ('specially organs), but often get stuck.
Mauls, two-handed swords, and halberds do the most damage, but I'm not quite certain if you can make these :roach:
(EDIT: Actually, Dwarves can't even wield them :smallsigh:)
The mace deals more direct damage than the axe, and somehow the sword does as well. The spear deals less damage than any.
However, direct damage is not an accurate measure of usefulness.
Internal wounds seem to knock them out with pain most often.
Getting an arm lopped off is particularly unhealthy.
It is very likely that a broken arm doesn't work quite as well.
I prefer slashing weapons, particularly the axe. In Fortress mode, I rarely have access to metal (not the case in my newest-I found a massive deposit of magnetite), and thus my military ends up with crossbows primarily.
But I
have used bludgeoning weapons in Adventurer, and they can be
very effective ("the head collapses into the body, an unrecognizable mass")
The largest factor is the dwarves' ability to use them.