From Diablo Wiki
All base bows have the same firing rate in Diablo and Hellfire.
Unlike melee weapon damage, bow damage is added onto your character's base damage from their attributes, rather than modified by it. A better bow lets the player deal more damage but the inflicted damage is not multiplied by the weapon, as it is for melee fighters. In the case of the Rogue, her base damage from strength and durability makes up the great majority of her total damage, so her choice of bow doesn't make that large a difference in the damage she delivers. For instance, a rogue with 300 dexterity might do 80-90 damage with a crappy bow, and 92-110 with a Windforce.
For this reason, most expert rogues use a bow that grants resistance, since that doesn't cost them much damage, and it makes them more flexible in their other equipment and jewelry. This also means that low level unique bows can be used even in the late game, though the generally lacking stats of most of the Unique Bows makes that less of a viable option. A Warrior couldn't consider using a dagger in hell, while a Rogue could kill adequately with a short bow, and would actually have the same minimum damage with a short bow as with a long war bow.
All bows look the same when equipped on your character.
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