Despite all evidence to the contrary, some gamers are claiming that Wii titles like Skyward Sword and Metroid: Other M look better on the Wii U than they do on the Wii due to the fact that the console upscales everything to 720p and 1080p depending on display. This is possible because of the Wii U's HDMI connection, which the previous Wii lacked.
The claim that games look better and that they're upscaled isn't entirely factual—which is to say it isn't true at all—because the games are still being rendered at a native render resolution of 480p. In other words, the games aren't being rendered in high definition. What you're seeing is a stretched out image that only serves to make the jagged edges all the more apparent on your HD display.
The only case in which the games have the potential to look better—subjectively speaking—is when you use the same display you used for your Wii to play those games on the Wii U. The picture quality is better simply because of the presence of an HDMI connection, not because of any built-in filtering or upscaling that's going on with the Wii U. In many cases, the games actually look worse than they do on the Wii U than they did on the Wii because of the upscaling.
If you want to get true high definition quality out of a Wii game, you'll have to use the Dolphin emulator on the PC to output true HD graphics. In addition to that, the emulator also allows you to replace the low resolution textures in the games with high resolution ones—if they're available. In addition to that, the emulator also adds support for anti-aliasing and anisotropic filtering, which are two graphical options that the Wii U's emulator for Wii games lacks despite having the hardware power to deliver.
It goes without saying that Nintendo dropped the ball on this one by not delivering much more than a straight up port of its Wii software on the new device. The publisher certainly could've done a lot more with it to cater to owners of original Wii titles in the same way that Sony added numerous upscaling filters for PSP titles on the PS Vita.
Note: The screenshot of Skyward Sword above was taken on the Dolphin.