As some have said, they're two different games and as Nate said, even two different mindsets.
I'll take Nate DaZombie's post, which captures exactly what I'm going for:
I can't decide, I play each one with a different mindset. With The Legend of Zelda, I am embarking on a epic quest to save the kingdom, vanquishing and who would try to stop me! While playing minecraft though, I tend to putter around, fixing my house, exploring some caves, and building better defenses.
In Zelda, you don't get very much freedom (I'm basing this off of Wind Waker and Link to the Past, both of which I have completed). Sure, you can name your character, maybe even change the color of link's outfit? But there's very little choice in how the story goes.
Minecraft on the other hand, gives you loads of freedom. But do you ever feel epic playing it? Sure, you might feel epic building the NCC Enterprise out of Voxels or fortifying your house. But there's no larger than life purpose to the game that you get out of Zelda. Maybe Uniqueness is the word I'm thinking of?
Maybe its comparable to Batman: Arkham Asylum and your typical Superhero Online game. In a typical super hero MMO you can customize your hero (name, look, abilities, etc) and you can go anywhere you want with your character. But you're one dude on a server with many other "unique" heroes. In Batman AA, you feel like THE Batman. But you have to follow its linear story and you can't do much other than just have fun along the way. Even the sequel, Arkham City, has more stuff to do, but its still within the confines of the game.
Those aren't necessarily good or bad things. To me they're equal trade offs. Do I want an epic story but no freedom? Or lots of freedom but no meaning to what I'm doing?