As a stealth character, I always go by the credo,
kill it in 1 shot
You want to do as much damage with the initial shot as possible so you won't need a second shot. Because of this, I tend to favor the bigger, heavier weapons over the lighter ones.
Having said that, if you were solely relying on bows as your source of damage, then you should be carrying two bows in the first place. From uesp:
time = 0.4s full draw * (1 + 0.1 * bow weight) / (1 + Quick Shot perk)
minimum full draw shot time = time + 1s
Here are some bow values with base damage:
- Longbow - weight 5 - 6 damage
- Hunting Bow - weight 7 - 7 damage
- Daedric Bow - weight 18 - 19 damage
Longbow weighs the least so shoots the fastest, but it doesn't allow you to use smithing perks to obtain the maximum damage.
Hunting bow is the lightest bow that you can improve to the max.
Daedric Bow does the most damage.
Using the above formula, here are the total speed it takes to do 1 shot (with no perks):
- Longbow - 1.6 seconds
- Hunting Bow - 1.68 seconds
- Daedric Bow - 2.12 seconds
For all accounts and purposes, the Hunting Bow is far superior to the Longbow since it has a much higher maximum possible damage value due to steel smithing with very little increase to total shot time. So now the choice is between the Hunting Bow and Daedric Bow.
Keep in mind the values you see are base damage, with skills in marksman as well as the archery perks, the final difference between the hunting bow and daedric bow will be amplified.
final damage = (base damage + smithing increase) * (1 + 0.5 * skill/100) * (1 + perk effects) * (1 + item effects)
Lets assume smithing adds the same amount of damage to both bows, so we can drop that modifier, we can ignore arrows for the same reason:
Lets also add in a 50% marksman damage modifier from gear since that's pretty easy to get:
Final damage values:
- Hunting Bow - 31.5 damage = 18.75 DPS
- Daedric Bow - 85.5 damage = 40.33 DPS
@Andreas is right, I shouldn't have dropped smithing and arrow bonus since it benefits the bow with the faster shot more:
Final DPS values with an arbitrarily high smithing and arrow bonus (lets say adds 200 damage):
- Hunting Bow - 231.5 damage = 137.797
- Daedric Bow - 285.5 damage = 134.670
Looks like at this point the hunting bow starts winning out DPS wise.
So the daedric bow not only does more damage per shot at low smithing but the hunting bow eventually wins out. However, keep in mind the higher damage from the daedric bow is increased by x3 from the sneak attack multiplier for roughly ~150 more damage in the end.
Use the Heavier (Daedric Bow) for sneaking
If you are facing a lot of small and weak enemies (swarm of rats, for instance), then you purely want # of shots per minute since doing high damage is overkill. In those situations, you will go with a longbow for the fastest arrow output.