Found a direct contradiction between Bungie.net and in-game destiny. Looking at the different scopes for a gun shows different results for how it effects your weapons between bungie.net and in-game destiny.
Here is a link to the third scope for Aethons Epilogue on Bungie.Net
You can see [url=http://imgur.com/aroibgO]Here[/url] that it says the Ranged Lens RLS3 will increase both Range and Stability on the gun, but when on my character in-game, it says that the stability decreases by using this scope. I dont have a screenshot of in-game destiny, maybe some else can get one for me, but go ahead and check for yourself that the effects are different between Bungie.net and in-game.
Which is actually true? I would really rather the Bungie.net be true because its really amazing, but I have yet to switch from the default scope because I cant take any more hit in Stability until I unlock Perfect Balance.
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Each scope will increases the stats in different ways. The scope you're currently using just increases stability more than the scope you're switching too.
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It increases your stability from the base stat but if you are already using a scope that gives you even better stability it will lower it.
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use the scope its worth it!