Vader already had a missing hand, so the voltage was going into his systems more directly. He wasn't sparing effort for defense. Sidious's lightning was stronger. TFU goes over-the-top with everything. Take your pick.
I don't think that Darth Vader is immune to effects of Force lightning. Galen Marek did overload the defenses of Darth Vader's armor with his lightning at one point.
Darth Sidious is superior master of the dark side then Galen Marek so the former is more specialized and effective in matters of offensive applications of the dark side accordingly.
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Yeah... basically because Sidious's lightning is more powerful, easily within the top three Sith practitioners of force lightning, while Starkiller is not.
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I wasn't including the Son, hence "Sith practitioners."
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Vader's missing hand isn't such a big deal, it was not as if Sidious directly bombarded Vader with lightning, Sidious was not in this position. Vader picked Sidious from behind which led to some of the latter's lightning bolts hitting Vader erratically and this was enough.
In a normal setting in which Vader is fine and Sidious unleashes his barrage of lightning on Vader in proper manner, I don't think that Vader can last.
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He had a missing hand against Starkiller as well, so that's not really an answer.
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No Starkiller cut off his hand.
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Shadilay my brothers and sisters. With any luck we will throw off the shackles of normie oppression. We have nothing to lose but our chains! Praise Kek!
THE MOTTO IS "IN KEK WE TRUST"