Does the Wii U do a worse job with those through emulation?
I do have a Wii, but even with a component cable the looks are not enough for me in a modern TV, that is why I thought having the Wii U HDMI port would make things look better.
Neither the Wii nor the Wii U use emulation. Both have the hardware to play GC games natively.
But keep in mind that the Wii U's upscale of SD content is not that great. It wont necessarily look better than using a Wii over component cables.
You could get an upscaler, but you know, 480p or 480i is never gonna look good on a 1080p or 4k display. You have the choice between very blurry, kinda blurry, or really sharp and pixelated. Most prefer the latter, but none look truly great I'd say.