Several short and to the point reasons:
1. You're in better control of a city/nation
You have more choices and many more freedoms on how things will get run, and you don't feel like you're kept down like in New Leaf as the Mayor.
2. Deep character interaction
Instead of just simple sending letters and gifts and occasional chats with the villagers, you actually grow closer to the characters in the world, and can later date, and even get married and have kids. Plus, no "animalese" all the time.
3. Dungeon exploration, Monster Taming, and battle
You have more than just fishing and catching bugs all day to do, and you have a farm as well that lets you more efficiently grow any number of vegetables or fruits. The Monsters you tame can help maintain the farm, and you can explore with them or NPCs when the chances are right. Classic RPG elements like choice of weapons and so on too.
I implore you to see Rune Factory 4 as the better game between the two, it's very worth the 40$ compared to the snore fest that New Leaf eventually becomes quickly.
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Except that Animal Crossing is the shiz and Runescape 4 or whatever crap you're talking about is terrible.