In fact, if you look closely, you will find that although the sword and dagger have the same damage (damage created per unit of time, or DPH), their attack speed is not the same, and all skills in D4 will have different release actions (different speeds and slowness) depending on the weapon chosen.
Faster weapons stack buffs & accumulate resources faster, and slower weapons can deal more damage in a single hit (often when you’re stacked at max). Also, different weapons will cause you to release the action and end the action in different frames, which can make a big difference in the feel of the operation (often the faster weapon is better).
But more importantly, different weapons offer different enhancements (look closely at your weapon, the sword says increased critical damage, and the dagger damage says increase damage to close range) to deal with different talents and builds. Some classes also have special passives to deal with different weapons, and we don’t choose weapons at random (as long as it’s 925)