Vary the damage bonuses of the artifacts from game to game, in order to prevent there from being clearly defined top-tier artifacts that players should always try to obtain, and bottom-tier artifacts that players should ignore.

For instance, this means that in a given game, Mjollnir might deal only 1d6 bonus lightning damage, while Snickersnee deals 1d12. Or Mjollnir could deal 1d18 and Cleaver deals 1d7. The only way to get an idea would be to use a stethoscope to identify how much damage is being done.

This does not address artifacts whose bonuses only apply to a narrow set of monsters and are often considered inferior for that reason.