i am at a stage where three of my characters are over 80 in there range and bow skills. now it comes down to whether to use double shot crossbow or some of these ncie bows i found like the hunters bow, demon string, strong bow, eagle eye bow. and etc.

#1 querrel from a cross bow dose more damage than arrows. but these special bows i found have added damage. and xbow's don't.

#2 though double shot xbow have 2x per round, but -4 initiative, and these speical bows mostly have +3 ot 5 initative, so i should be getting more shots with these special bows (maybe at least 2 or more )

in live test i couldn't really tell. some times the bow fires 3x, some times the xbow fires 3x or 2x it varies. even in the same character.

so what is the advice on which ones to use.

Well the double shot x-bow can also be turned into a triple shot, IIRC you need another light crossbow and a Gadgeteer with an engineering of at least 70 to do it. The triple shot is a true machine gun. If the character is a Ranger, it will open up the most chances for doing criticals from the sheer number of shots it takes. Its downside is it drains stamina pretty fast (if you have a female ranger with endurance regen items it's not so bad). Really you can't go wrong with either choice, they are both great ranged options.

Another downside about 3-shot crossbow:
I think you hit a lot less with a triple shot cross bow than with a normal bow. Sometimes the arrows just go up in the air, then it goes down on the ground. This never (or very rarely) happens with a normal bow (or crossbow(?)).

I equipped Vi with the demonstring... and she didnt have a single point in bow... here I am about 10-12 hours later and she has about 25-30 in that skill, no points added... IU dunno if this is the kinda thing that you wanted to know about but there it is

The big concern with the Triple-shot xbow is the amount of ammunition it burns through.

I played a game with a ranger, 90+ bow skills, high dex, high senses, 125 speed (with haste), and he emptied 100 xbow bolts in far too short a time.

If you have more than one bowman in your party, and do even a moderate amount of long-ranged combat, using the triple xbow will be difficult just because you'll have to carry around an obscene number of bolts, which will weigh down your party tremendously.

Personally, I prefer having 1 ranger using a bow and relying on magic for long ranged attacks whenever possible. Carrying ammunition for 3 or more people is just too much of a hassle.

If you're using a Ranger, keep Bows on him. Bow weapons have more bonuses and special attributes than crossbows. Reserve Crossbows (tripleshot, etc) for those who will be doing more melee than ranged (fighters, lords, etc). That way you won't be consuming that much ammo.