Axes chop bits off. This is usually my preferred weapon, because once an enemy has lost and arm or leg (besides FB/Titans) it's more or less dead, as the bleeding will soon claim it.
Spears poke nasty holes. This can deal serious damage to internal organs on organic enemies, which can quickly lead to incapacitation and death. However, many creatures can ignore their organs being ripped up (the less essential ones anyway, such as the guts, liver, pancreas; anything but the heart, lungs and brain), and thus can still be a threat. Thus I don't use spears much.
Swords are a cross between axes and spears; they can lop bits off and poke at organs, but aren't as good at either. I never really use them.
Hammers are for dishing out pain, thus I love them. They will go through most any armor (even copper hammers can give a steel-clad enemy a very bad day) and instead of creating salsa, they just bash every bone to bits. This usually means that the enemy in question will not die until it falls over from pain, at which point it will probably get an unwelcome bit of metal lodged in its brain forthwith. It also means less bits to clean up afterward.
Crossbows are an excellent support weapon, especially if the marksdwarves are kept in a safe and secure location they can fire from and won't be inclined to run up to the enemy from (I use pillboxes). Crossbows will often incapacitate and enemy with a shot to some organ (they pierce nicely, like spears) but I rarely see them get killshots with any regularity, just moments of dwarven badassness (like my militia commander shooting an entire ambush dead by himself, leagues from the fortress and his allies).
For my personal preference, I'll usually have at least one squad of crossbowmen and one squad of either hammerdwarves or axedwarves. Often the crossbows will do a decent job stopping the advance, and the melee are then sent in to clean up.