Simple stat variation is one element, but it can be stretched much further to change the elemental theme of artifacts and the abilities given. For example, here is the Staff of Destruction:
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Staff of Destruction (15-18 power, 4 apr, cold damage)
Type: weapon / staff
15 Power [Range 1.20] (+150% Magic), 0 Attack, 4 Armor Penetration, Crit 0%
Damage type: cold
When wielded/worn:
Increases damage type: 16% fire,14% lightning.
Spellpower 10, Spell Crit 15%
Damage type = cold OR darkness OR arcane OR fire
Power = 12 + 2d3
Increases damage type: 10 + 1d10 % of 1d3 elements (fire/lightning/acid/cold)
Spellpower = 8 + 2d2
Spell Crit = 10 + 2d5 %
10% chance of Mana pool increase (say 10-20 Mana)
10% chance of Magic stat increase (2-4 Magic)
Suddenly finding the staff is more interesting. It could be stronger than currently, or it could be weaker. Notably it won't be a *lot* stronger or a lot weaker, since it has set boundaries and a strict theme.
The same principles can be applied to a great deal of artifacts. Ringil, for instance, could be randomly generated as a different one-handed weapon type. It could have a fire theme that allows you to cast Flameshock and increases fire damage. Or a lightning theme that casts chain lightning. And so on. Each artifact can be defined to have varieties in their effects between games, whilst still staying the same sort of item with similar abilities. This is done without any major balance worries, and without turning artifacts into junk.
It'd quite easy to go through the whole list of current artifacts and suggest these sort of variations, with the exception perhaps of a few story-related items.