I think they're both excellent games. I usually think DAI is better, though not always.
Reasons I prefer DAO:
Silent protagonist
Full text dialogue options
Art style
Slower pace of combat
More freedom to engage in conversations wherever I like
More varied combat options
More varied character development options
Moddability
Dev Console
More symmetrical combat mechanics (thus making friendly fire manageable)
Combat abilities, on their own, are more fun and interesting
Melee rogues
Warrior archers
Can play without having a weapon equipped, and there's sometimes an actual combat benefit to doing so
Reasons I prefer DAI:
More exploration
Better level design
Plot less immediately visible
Plot less immediately mandatory
More freedom to design player character's response to situation
More traditional party dynamics
Free-roaming camera
Bigger
Combat and conversation make up a smaller proportion of total gameplay
Crafting
Race-specific armour
No auto-healing
Combat abilities, interacting with each other, are more fun and interesting
Archery
Can engage enemies at greater range (largely a result of greater draw distance)
Non-cinematic conversations
Fewer cinematics (none? I don't remember any) showing events the protagonist doesn't witness