How does my choice of weapon matter?

Weapons have become accessories in Diablo 3. Since the game is designed to prefer magic skill attacks over melee, the weapons work like your pants or hat—they add to your stats and attributes, though you may never swing your weapon as a melee attack. You can set melee to a hotkey if you want, though. In your example, yes, the bow and dagger are equivalent. Elemental damage modifiers are added to normal damage. It's all about raising DPS unless you desire an attribute modifier.

May seem obvious, but there are also skills that require a specific item type to become usable (e.g. Demon Hunter's bow abilities will not work with a sword or other non-bow weapon equipped). I presume this is true for other classes as well, so in that case choosing which weapon to wield matters quite a bit, at least for Demon Hunters.