All this time, I thought silver does more damage to vampires. Turns out that's not the case. What does then?
Silver is for werewolves.
Fire spells and weapons with fire enchantments are most efficient against vampires.
This is because vampires have a 50% weakness to fire damage (opposed to a 50% resistance to frost damage)
Source: Skyrim wiki/Vampire page
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Thanks! @Mathias711 clarified that as of 1.9.32.0.8, they also deal the bonus damage against vampires. Time to find myself a fire-enchanted silver sword (heh). – user400424 Mar 25 '16 at 10:39
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2@user400424 One of my higher priorities in Skyrim is going to Ironbind Barrow and learning the Fiery Soul Trap Enchant. 10 points of fire damage per hit and fills soul gems. You also get a relatively high number of hits for the soul power. – tjd Mar 28 '16 at 14:04
If one has the most recent patch (1.9.32.0.8), silver weapons also apply their bonus damage against Vampires.
. This bonus damage is 20 extra base damage – Mathias711 Mar 25 '16 at 10:30