See, this is a difficult topic. Skyward Sword has shown that linear overworlds can turn away plenty of fans. It's not necessarily a bad thing, depending upon the game, but The Legend of Zelda is best nonlinear in my opinion. However, it's important that they make the best of the open world. Twilight Princess also set a precedent about too little in an open overworld.
I'll get this out of the way. Zelda U should certainly have an open world. However, it's more than just emulating Arkham City like you're suggesting. As a Batman fan, I'm well acquainted with that game's overworld. I felt like Arkham City, like Twilight Princess, had a bit of an empty overworld. I was expecting more fights with thugs, and I found a lot of altercations to be few and far between.
What I think would be a good overworld to emulate would be Assassin's Creed. Yes, I'm a huge Assassin's Creed fan, and it might be what's making me lean towards that, but when you look at Assassin's Creed's overworld, you find cities filled with city guards, all of whom may become hostile with a slightest crime. Zelda U should definitely strive for an overworld filled with enemies to fight.
However, in Assassin's Creed, they don't immediately engage you in combat; you either have to be notorious, or commit a crime. Therefore, it can have more enemies on-screen. Zelda, though, has enemies that attack on sight, so it would be important to not fill the overworld with too many enemies.
On the other hand, the overworld should be filled with hidden treasures that vary in rewards. More obvious treasures with small rupees, and the hidden ones deep in mini-caves containing Heart Pieces, or high-value rupees. It also wouldn't hurt to do what Twilight Princess did and have a few caves to explore. But there should be more than what we saw in Twilight Princess.
So yeah, an open world is ideal, but it must be done right. I'm sure Nintendo will do fine with the construction of Zelda U's overworld; they've done it plenty of times before.