I just found one at level 14 on my shotgun charecter. Should I use this or my combat shotgun? They do the same amount of damage (about 105) but the never ending double barrel has about half the range.

A never-ending means you never have to reload, which is the double-barrels biggest flaw. So yes, use that until you find a Combat Shotgun.

The biggest advantage that Shotgun will have over the Combat Shotgun is if you give it a Sawed-Off Barrel and a Calibrated Powerful Receiver - critical hits will be devastating with it. Does the Double Shotgun have a lower VATS cost than the Combat Shotgun?

I dig the never ending weapons because you can stock up on a whole bunch of ammo, throw it on the weapons workbench and get it just right and then unleash hell.

I'm 95% a melee player...smash faces with a super sledge (Daddy Sledge w00t!) but if I decide to use a gun, I have a never ending laser rifle pimped out to the max and I'm always loaded with like 1500 rounds fusion cell so I just unleash hell lol

Double Barrel Shotgun's have a much less VAT's cost than the Combat Shotgun. I even changed my Instigating Combat out for the Wounding Double simply for this fact, until i find an Instigating Double that is I think the Combat Shotgun is much more viable if you have a couple of VAT's enhanced Legendary armour items fitted along with a Powered armour piece (10% reduction cost for the enhanced and increased AP recharge rate for the Power).

Combat Shotguns will do much more damage with the later weapon mods so its a case of picking your time to swap them over, personally I always stick with the Double over the Combat, it makes life a little more interesting and certainly more difficult in some circumstances

Combat Shotgun will do more damage and since I don't use VATS with shotguns (why would you need to?), I would stick with the Combat Shotgun myself. However, the Never Ending Double Barrel has it's moments and can be very fun to use.

The unlimited legendary is amazing for the slower reloading weps.

I had got a .44 with unlimited and its just fun not needing to reload lol

I actually enjoy the reload animation of the .44 Revolver myself.

Its already a very slow gun without needing to reload it

I love the reload animations for rp purposes and because its fun for some reason lol