At their core, the Wii U/3DS versions, and the Wii version, are the same game. The level design is MOSTLY the same (more on that later), and the story and characters are the same too. The main differences come in how you control the game.
Essentially, in the Wii version, you mainly control Rodea by pointing the Wii Remote at the general area or target you want to fly towards. Rodea will then automatically fly towards the location or target you marked, and he can fly infinitely. The only limitations his flight has is that you need to reset your flight path if you fly for too long without hitting anything, and there must be a target withing range for you to be able to fly towards it. You can also perform a Boost Attack while flying (essentially Sonic's Homing Attack turned up to 11), and can also use the Machine Gun Power Up to shoot while flying if you happen to have it. And you can run around with the D-Pad when on the ground (which feels a bit stiff, but it doesn't matter since you rarely need to walk). The Wii version also has a Mario-esque health system. You start off with white hair, and a small tail, which is your normal state. Collect a tail item, and Rodea's hair turns a neon green colour, and his tail grows larger. This gives you an extra hit point, and double damage from attacks, and you fly a bit faster. If you take damage in the default state, Rodea's tail breaks, and he can only fly for really short bursts before needing to reset the flight path, and he also cannot attack. There are of course more abilities and power-ups to use, but this is the basic gist of how you play. While this is definitely a new and unique control scheme and can be daunting at first, it's very intuitive in practice and you'll be zipping around levels at great speeds before long.
The Wii U/3DS versions completely change how the flying works. Basically, instead of running on a targeting range system, it runs on a fuel system. You have a much wider targeting range, but you also can't fly forever before needing to land on solid ground and recharge your flight meter. Rodea also flies much slower by default, as the game incorporates an upgrade system where you collect materials to upgrade Rodea's specs. And by default, everything is in a poor, sluggish state, and some enemies you could one-shot in the Wii version, take multiple hits to defeat in the Wii U/3DS version until you upgrade enough. All of this combined with the fuel system can really make otherwise natural sections of the levels, feel incredibly awkward and frustrating because you can easily run out of fuel before you can hit some ground. Also, the simple process of setting your flight path is also slow and awkward. In the Wii version, you simply point somewhere with the Wii Remote, click B, and he's off. In the Wii U/3DS version, you have to jump, press A in mid-air to make Rodea float on the spot, and then you have to slowly use the control stick to try and aim precisely where you want to go, and then he flies at a snail's pace. Rodea can also fly straight up in these versions by pressing Y, but the levels were not designed with this feature in mind, specifically vertical sections, and you can completely cheese sections of the levels with it.
On the level design, it is the same at it's core between versions, but there are differences. First off, the Wii U/3DS versions increase the scale of levels by about 2 or 3 times. I do not mean they added things to the levels. I mean they literally took the level geometry of the levels into their 3D model editor, scaled them up by 2 or 3 times their original size, and put them back into the game. They didn't add extra details to fill out these huge expanses. They are just bigger, meaning it takes longer for Rodea to get from place to place, and that's
before you consider that he flies slower than in the Wii version until he's fully upgraded, and before you consider he has limited fuel. This means levels take more than twice as long to complete. Oh, and they applied this to already huge giant bosses the game has too, and those are INCREDIBLY frustrating when you fly slower than the Wii version, and have a fuel system.
They also removed various things from the level design, such as level specific gimmicks that the Wii version had, which was probably because they knew the Wii U/3DS controls couldn't handle them, but this removes the challenge from some areas. The biggest offender of this is IIRC, Chapter 21. This is near the end-game, and you are essentially flying toward's the big bad's base in an on-rails shooter section. This section is in both versions of the game. After this though, you land on the tower. In the Wii version, the entrance inside is locked, and you have to explore the surrounding area to find some keys to get in. There is of course plenty of enemies, obstacles, secrets, and just general level design to find at this point. However, in the Wii U version, they COMPLETELY removed all of the level design here. There is no locked door, you can just walk straight through the door and finish the level. The only thing they kept were the secret medals to fill out the medal quota, but hunting for them is completely boring because they removed all of the level design, and like I said before, all of the geometry is made extra huge in the Wii U/3DS version. In case you don't know what I mean by "removing the level design", imagine a Sonic level where they removed all of the rings, springs, boost pads, enemies, item monitors, and other stage objects, and only kept the basic geometry. This is literally what they did to this Chapter of Rodea, and it's SO CONFUSING. Like I can't fathom why they did this. They basically removed a level from the game.
Also, there are bonus doors placed in the levels in both versions. In the Wii version, these take you to 2D side scrolling sections with Gravitons (this game's equivalent to Coins or Rings), and a medal at the end. They're very reminiscent of Crash Bandicoot bonus rooms, but you can fly. The Wii U and 3DS versions remove these bonus rooms, and replace them with a guessing game, where 3 launch rings are placed and will fly you on one of the 3 paths, one leading to nothing, one leading to loads of Gravitons, and one leading to materials. It's just a guessing game that only works because of the inferior draw distance in these versions, and doesn't require much player input.
Moving on from the gameplay, the graphics are worse in the Wii U and 3DS versions too.
Left is the Wii U version, the right is the Wii version. As you can see, the Wii version is colourful, lush, and vibrant. The Wii U version (which is a ported 3DS game), while it does have a higher resolution and has this cel shaded, sketch effect (like Valkyria Chronicles), looks totally drab and lifeless in comparison to the Wii version. Also, for some reason, the sky in some levels in the Wii U version looks like it's full of Mako from FFVII, and I can't fathom why. It's just a normal sky in the Wii version, but takes on this weird colour in the Wii U version.
This also applies to the pre-rendered cutscenes, and even the character portraits, for some reason.
The Wii version also runs at up 60FPS. It usually runs at more around the 30-40 range, but it never goes below that to some unplayable state. The Wii U version runs at 30FPS but frequently goes much lower. And the 3DS version runs at more around 20-25FPS at the best of times (though I've heard it actually runs better on a New 3DS).
And finally, the Wii version has a local multiplayer mode. It was completely removed from the other versions.
This isn't even all of the bad changes (and I will admit that there are a few minor things the Wii U version does better), but it's the biggest ones, and should illustrate how they butchered the port.
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