HGSS:
Battle Tower
Battle Factory
Battle Hall
Battle Castle
Battle Arcade
Trainer House
PokeGear Trainer rematches (including 16 Gym Leader remaches)
Pokemon League Rematches
Pokeathlon minigames
Voltorb minigame
Safari Zone
Red rematch

ORAS:

Battle Maison (Single, Double, Multi)
Triple Battles
Rotation Battles
Inverse Battles
Battle Institute Battle Test
Mauville Food Court
Trainer Eye rematches
Pokemon League Rematches
Wally Rematch
Battle Resort Type Specialists rematches
DexNav chaining/ reaching Platinum rank
Super Secret Bases customization/ daily battles/ flag collecting
Contest Spectaculars
DexNav chaining/ reaching Platinum rank
Pokemon Amie feeding/ petting/ playing faces/ + 3 minigames
Super Taining minigames
Soaring + Mirage Spots
Delta Episode

And some anons dare to say HGSS has more content than ORAS.