I'll start with what's obviously different. The realistic, brown style from Twilight Princess is gone in favor of a style that is sort of cel-shaded, and sort of painterly. The Link model is realistically proportioned, but brightly colored and low on detail. The world is extremely colorful, with an impressive depth of field effect that makes the backgrounds appear more painted in the distance.
The controls have been revamped to make use of the Wii MotionPlus, and to allow for quick, easy play. The sword is mapped directly to Wiimote movement, using both the pointer and the MotionPlus. I later found out at Nintendo's developer roundtable that pointer support was removed from the E3 demo to avoid interference from the bright lights of the show. This detail is important for a reason I'll go into in a bit. The sword "charges" when you hold it out in any direction, and swinging it when charged releases a circular energy attack. The shield is mapped to the Nunchuk, and can be used for a "shield bash" move, or paired with a sword swing for a spin attack, either horizontally or vertically.
The other major control change came with the sub-weapons. Bombs, slingshot, the whip, and other items are mapped to a radial menu that pops up when you hold B. You then point at the item you want to equip and press A, then press B to use it. It's infinitely quicker than the usual Zelda inventory, and it's a nice change. It's an obvious change, in fact. Why didn't this happen before? It's so nice for the flow of gameplay to be able to switch weapons on the fly. All of the weapons use motion, as well -- bombs use an over- or underhand tossing motion, the whip uses flicks of the Wiimote, and the slingshot is controlled by pointing. The new item, the "beetle," is flown by tilting.
Every interaction in the game is tailored to the motion interface. Enemies very clearly require you to swing the sword in a certain way. Deku Baba plants have mouths that open in a certain orientation, and you have to slice along that mouth. Goblin enemies will hold their swords up in such a way that you have to slice parallel to them to avoid being blocked. Even the door to get into the boss room requires you to spin the sword. The boss, of course, has vulnerable claws that you have to slice between by slicing in the proper direction.
Even with the new controls, however, the demo seemed to fit comfortably within the 3D Zelda paradigm. The movement of the character was similar in speed and execution to previous games, and the enemies all fall into the "Use that thing you just got or learned about" category. Even the puff of smoke when an enemy dies was familiar. Even with new controls, it felt likeZelda. Aonuma said that the game was being streamlined to focus on having fun interacting with the game, rather than getting lost, which makes it sound like there will be smaller, discrete areas to explore, but that's hard to evaluate in a tiny demo.
The controls were a bit of a problem, at least for me. Link usually refused to slash in the direction I slashed. If I moved the Wiimote slowly and deliberately, I could pull it off, but he often went for an odd diagonal instead of a straight horizontal or vertical slash. Other Joystiq staffers didn't experience this issue, so it's possible it was a calibration issue on my end. If the pointer will be helping it along in the final game, that should ameliorate the problem somewhat.
Based on what I've seen, I'm somewhere between cautious and cautiously optimistic. The sword controls didn't do much for me, but the controls for every other item were great. The game design doesn't seem to have changed much, but there's the promise of a focus on fun over the cruft that has come to dominate the series. And that style is eye-catching.