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
A Smithy enhanced bow/sword with fire enchantments works great. I got some great weapons from Oblivion, Ebony Bow/Sword, and upgraded them at Smith with ebony ingots. Bow deals 102 base damage now, (Legendary upgrade), and sword is 58. Both called "of the inferno," they also do 45% fire damage. Wicked. Add ebony arrows and if you have archery perks, and enchanted armor for more archery damage (Eleven Bracers of Eminent Archery), Bows do an extra 35% damage. Drink archery potion, and it's a one shot deal...for most levels of Vampires...perhaps two on really bad guys.