Is that because of resistances? I would think that most enemies and bosses have less resistance to lighting or fire damage vs physical damage. Is that not true?
Also, which stat affects bow and arrow damage? Does any stat affect firebombs and other throwable consumables?
There are a lot of variables. Enemies have resistances to certain types of elements as well as certain types of damage (slashing, crushing, etc). And, your character's stats also determine the scaling of elemental damage (faith raises dark and lightning, for example). Bows generally scale with dex, but also have a strength requirement and scale with strength some as well. The arrow element also is effected by the scaling of your stats plus the damage it does. Also, stated damage on the weapon is generally worth more than damage you hope to get via stat scaling. The club vs mace is a good example. At max level, the club has a low S strength scaling while the mace has a high A. You'd think that at like 40 strength the S would make a difference, however the mace's damage actually makes it hit harder, despite having the lower scaling.
Certain bosses have different resistances and some things work better than others (a certain demon who smelts is very resistant to dark and lightning, where a certain dragon who is guarding is extremely weak to lightning and especially dark; the same spell does around 250 damage to one and 1250 to another.). And it isn't always the case you would suspect either, as in previous Souls games certain fire demons were actually weak TO fire damage.
Also, something to take into account is what part of the weapon you hit with. If you're using a pole arm (halberd and such), hitting them with the pole part won't do nearly the damage of hitting them with the bladed part.
Another large considering is move set, swing speed, stamina usage, and how effective YOU can wield that weapon. If large, slow weapon does double the damage of a smaller, faster one, but you can only swing 1/3 the speed, you're losing actual DPS, but hitting harder. This might be good for PVP, but in a PVE environment, that is wasteful.
Lastly, don't forget about Fashion Souls and what you like playing with.