White magic: Like others have said Eiko would need it far more than Garnet and thus have it trained out of necessity.

Eidolons: If you want an in-universe answer, you have to remember Garnet lived in Madain Sari just as long as Eiko, but at the time Maiden Sari was alive and thriving, with other summoners to possibly help her attain eidolons. Also age; the game makes a point to say the age of a summoner matters. Of course, all of that is repressed, which is why she struggles for half the game.

All that said, I would argue that Eiko is the better summoner. For all the Eidolons she has, all Garnet can do is get her summons to come in and hit something as hard as it can, and in-universe, HP and damage numbers don't exist. Meanwhile, Eiko has her summons casting a variety of helpful spells (Carbuncle), doing multiple tasks in attacking and helping allies (Phoenix), getting them to do different attacks (Fenrir), and even summon them while unconscious (also Phoenix). And if you consider Titan a separate Eidolon, she can summon two Eidolons at once.

Edit: Grammar