Well, since these involve a video game, they can actually be codified.
In The Legend of Zelda: a Link to The Past, each sword upgrade generally doubles the damage dealt - the basic sword does 2 damage with a swing, while the final sword upgrade does 16. The Master Sword (and each upgrade beyond it) additionally offers increased reach and the ability to shoot beam attacks when at full health.
In general, the sword upgrades in Zelda games function much like sequential +N weapons - they have a linear upgrade path, offer increased reach (thus, accuracy) and damage, and confer generally only minor benefits beyond that.