Garnet's Eidolons > Eiko's Eidolons
Garnet's White Magic < Eiko's White Magic
Both have specialty.
That's why there are two characters with same job.
Garnet have 8 summons while Eiko have 4 summons.
All Garnet's Eidolons is attack-base, that'll make Garnet a mage-fighter (White Magic and Attacking Eidolon).
Eiko's Eidolons is offensive/healing-base, Madeen and Fenrir deal a damage while Phoenix and Carbuncle support your party, that'll make Eiko a healing machine.
And Goldenboco is right, Ark is a better summon than any of Eiko's.
White Magic can be useless in FFIX after you got Auto-Regen (You know how Auto-Regen works, right?).
Another reason Garnet is a better summoner than Eiko is her trance, Eidolon, if Garnet is a worst summoner, Square should have give her another trance. The same goes for Eiko's Double White Magic.
In my conclusion, Garnet is not a weak character, FFIX give importance to all character.
Nevertheless, I still prefer Eiko in battle but if I ever repair my PSX, I will start a new game consist of Zidane, Vivi, Garnet and Eiko.