My main character is a lvl 60 2h warrior and bow assassin and with Dawnguard I've come across a difficult decision as to what bow I should use.
Both have the same base stats. The Dragonbone bow has a faster draw time, quiet shot and goes well with the suit of Dragonbone armor I just made(I normally use Daedric). On the other hand the Crossbow can be immediately fired, has longer range and a greater abundance of ammo.
I would prefer to use Auriel's bow, but it is one of the worst stealth weapons in the game due to it's arrows exploding which leaves me with these two.

I say the crossbow, but I haven't played Dawnguard yet for a good feel for how each plays. One question for you, on that note:

Do you normally oneshot your enemies with the bow, or have to launch another shot or two to finish them off?

This should be on dawnguard section, moderators will probably move it

or you could do bound bow, isn't that more powerful than both?

I don't use conjuration.

And I don't see why this should be moved, it's just about two bows that I use for the normal game.

Enhanced dwarven crossbow is better. Higher base damage than dragonbone bow and has higher speed.

Longbow is better for killing multiple or lightly armored enemies and the crossbow is better for one shotting bosses or enemies in heavy armor. The crossbow takes a long time to reload without the fast reloading perk for archery.

This is why I asked if he oneshots most enemies or has to hit multiple times. If you oneshot go for the one with a faster, more accurate and longer shot, the crossbow, which I have seen enough DG gameplay vids to know functions more like a gun and less like a bow. If you have to hit multiple times use the one you can fire more often.

Daedric Bow FTW!!!!!

lol

I read somewhere that there is a bug when enchanting the enhanced dwarven crossbow. If I remember correctly, something about not ignoring 50% armor or something.

According the UESP wiki, the dragon bone bow has a draw speed of .75 which is equivalent to a dwarven bow. By way of contrast, the Daedric bow has a draw speed of .5 (Longbow has a draw speed of 1) The Dragonbone bow is clearly the best bow in the game, with a faster draw speed and more base damage.

Arrow type is much less important since most of the damage is coming from the bow, not the arrow. Nevertheless, dragonbone arrows are plentiful and free: just go to dragon lairs when you are running low and kill a dragon or two. Or fast travel to know dragon spawn spots, like the Stormcloak camp near Dragon's Bridge. Getting dwarven bolts for free requires raiding some dwarven ruin for scrap metal and whatever you can take off the Sphere Guardians.

For followers, DO NOT USE ENHANCED DWARVEN CROSSBOWS! For some reason they won't fire them. Instead, use enhanced STEEL crossbows. For followers you should definitely equip them with a crossbow since normal bows are bugged where they revert to their default hunting bow.

After playing around for awhile, I opted to stick with the Dragonbone bow. I like the drawspeed. The damage difference is negligible. And I found it easier to restock ammo.

I probably won't use the Crossbow again until they fix the atrocious placement of the bolts. It's like in your orbit or something I don't even know.

At least in my game, Dragonbone weapons can't be tempered (improved) as good as normal materials. Shame really.

You either have a mod, or a bug. They have the same tempering properties as dragon armor and the same perk.

The Enhanced Dwarven Crossbow is better. It has higher base damage, 50% Armor Penetration, has a much higher chance to stagger your opponent, fires faster and more accurately, and can fire Explosive Bolts. The only downside, is the longer reload time, which slows your movement down while you reload.

my dragonbone bow does more damage then my deadric or the enhanced cross bow. all three are crafted to legendary. but the difference is not much. maybe 8 points of damage difference.

Well what's cool with the crossbow is that if you have the Power Shot perk from the archery tree, ennemies stagger 100% of the time !! The damage is just as good as the best bow, and it can be higher if you use alchemy for overpowered potions of course
The downside is for stealth, it actually makes a lot of noise... the enemies go to you rather than to the spot where the projectile was fired ... So use it when there aren't too many enemies around (for stealth kills at least)

Why not use both depending on the situation ? Just put the two in your faves and you cann judge which one is useful, and when (:

I carry both for different situations.

With a Crossbow and Normal Bow, I barely need to ever fall back on melee.

Crossbow, you get stagger and armour penetration.

Seems to me that the unique bow from the new Dwemer ruin is the best bow in the game, considering its enchantment.

It is just Dwarven in quality, and if you have the quick shot perk then the enchanment is redundant.

I carry both, also. If I need to be quiet, I use the dragonbone bow. If it is a pack of enemies, I summon my Dremora Lords and fire the enhanced Dwarven crossbow. "No match at all", they exclaim. I absolutely LOVE the sound that the crossbow makes when fired. It is such a satisfying sound that gets me excited every time I shoot it. I have to switch between them because I can only stand so much excitement!