The touchscreen menus is something that cannot be understated. It makes the game so much faster and more exciting when you can equip four items in 1.5 seconds.
The gyroscope aiming is another thing that makes the game a lot more fast-paced and thrilling. I never liked the joystick aiming and I'm so glad to have a better, more quick and responsive way of aiming.
The graphics aren't just "better", they used the better technology to make a MUCH more detailed world. Almost every wall in the game is filled with tiny little details, from Malon's bedroom to the most obscure nooks and crannies of the dungeons. This feels much more like a living culture and world than the original game did by far.
I like the animation personally so I can't really refute that. Though, I will say that it is occasionally TOO smooth. If you don't do it precisely, Link takes a good second to turn around in the direct opposite direction. In the N64 game, he would just "snap" to whichever way you put the joystick. Here, it's the same, but it's a lot more finicky and most of the time Link actually walks/runs in a small circle to turn around. It looks better but it feels a little sluggish in my experience.
That's not to mention the more difficult Master Quest being a part of the game, and boss rush mode.