It goes without saying that the strongest one here is the Dragonslayer Greatbow with its special ammo. But at 10 weight, greatbows are pretty heavy and don't fit most people's builds. I won't bother even touching on crossbows too much, as they are less valuable (including the sniper crossbow which is also heavy -- 8 weight).
Crossbows VS Bows: The crossbows are faster but cannot aim. Bows CAN aim though, thus making them much more useful. This is kind of ironic considering that the "sniper crossbow" can't be used to aim at enemies.
(If want to know how to aim, note that you need to use your bow two-handed).
Anyway, this page will focus mainly between the two best every day use bows -- Black Bow of Pharis and Composite Bow.
The Pharis bow has an increased range AND a ParamBonus of S for Dexterity (the strength bonus is E). This scales well for a dexterity build / quality build. The composite bow has a C scale bonus for both Strength and Dex so this can be great for a strength character build. However, it has a decreased range. On the bright side, it DOES shoot faster though!
Composite Bow (CB)
+ C bonus for strength
+ Faster shooting (best bow for PVP)
- Shorter range
- C dexterity bonus
Black Bow of Pharis (BBoP)
+ Longer range (lurer enemies / snipe)
+ S ParamBonus for dex
- Slower shooting speed
- E Strength bonus
And there you have it. BOTH weapons have their purpose in the game and pretty much work in either situation.
Q: Is the Darkmoon Bow good?
Yes, the DMB / DB is good. But I honestly can't recommend it over the two bows mentioned here. It's not as strong as the composite can be and while it is faster than the BBoP, it just doesn't scale well in the end (E/D/-/D). Maybe worth trying for a faith build. You can make this by killing Gwyndolin -- the leader of the Darkmoon Convenant and using his soul and a +10 bow to create this weapon via the Giant Blacksmith.
Q: Is the Avelyn Crossbow good?
It's ... an ok repeater crossbow. It wastes bolts like crazy since you shoot three shots at once. These shots are weakened though as to not make the weapon overpowered, but are still very strong. If you manage to hit your opponent with all 3 at once, then it's worth using. But a lot of the time that's hard to do (such as in a PVP situation). I personally do not use it...at all. You can find it in The Duke's Archives.