The only trials weapon that is worth any sort of a -blam!- is Doctrine of Passing.... And perhaps the heavys. Trials weapons aren't good because they have a limited amount of perks they can roll and many of them are not good because of that. For example the shotgun, has no ranged tree perk and is same arch-type as the new IB shotty and that thing completely outclassed the ToO shotgun simply because the perks it can roll. Just curious, what sort of "secret" stat do these trials weapons have to make them superior?

No one said anything about secret stats. Did you even read my reply? Take a trials weapon. Now take the nl shadow, same arctype with the exact same skills. EXACT SAME SKILL TREE, the lamp will naturally do better more easily. The shadow with better skills then it will do better.. it's not that hard to understand. Bungie coding the weapon to work just alittle better under those circumstances is only natural for weapons such as those.