I tried the HDMI adapter, and I didn't like it. First, it only output to 720p, which my TV at the time didn't support (only 480i, 480p, and 1080i).
The other thing I didn't like about it was that it got HOT --- and FAST!
I've had no problems with the component cables. If my TV did support 720p, I would have guessed that the there would be no "better result" visually. Since the most the Wii can output is 480p, upscaled or not, it's still a 480p image and shouldn't look better either way.
If you need a good pair of cheap third-party cables, you can pick one up for less then $6 usually from amazon: http://url.llaffer.com/component
[EDIT] Looks like the price did go up a little, it's slightly over $6. Still, cheaper than if you bought first-party cables from GameStop or Wal-Mart. I've had mine for almost 3 years and have had no problems with it.