What’s the difference between the +100% and +120% eidolons?
The +120% eidolons have the same base bonus of +100% elemental attack, but gain an additional 4% elemental attack for each sub-eidolon of the same element that you have equipped, for a maximum of +120% elemental attack. A December 2019 update is expected to augment this bonus to 8%/sub-eidolon (maximum +140%). The +120% eidolons also have different summon effects, so in some circumstances a +100% eidolon may be preferred over a +120% eidolon (e.g., Hraesvelg’s -20% DEF debuff will often increase damage more than +20-40% elemental attack).
The Dark and Light +100% eidolons have a +80% base bonus, reaching a maximum of +100% with 5 matching-element sub-eidolons.
Both +100% and +120% eidolons are further augmented by limit breaks, increasing their base bonus or max matching-element bonus (Managarmr, Anubis) by up to +20%. Limit breaks can be added by using the eidolon limit break item obtained from Guild Damage Competition events (coming in August 2019).