Increased Item Rarity is an effect that increases the average number of affixes on items, resulting in more rare and exalted items. It also increases the chance of finding unique and set items.
Increased Item Rarity modifier is most commonly seen in the endgame system Monolith of Fate.
Similarly, there are effects like "Increased Amulet Drop Rate" which are typically granted by Blessings that you can obtain from the Monolith of Fate. This would cause more amulets (including uniques) to drop for you without affecting how many items of other types drop.
Modifiers that increase the quality or quantity of found items like "Increased Item Rarity" or "Increased Amulet Drop Rate" do not compete with modifiers that grant character power.