The advantage of using this adapter is to avoid interference with component-video cable. With the HDMI output, the signal is digital and interference-free (or at least more protected). I am unaware of any extraordinary gain in quality when using this adapter, as the final quality can not be greater than what the Wii can do himself. That is, the adapter enables bring the highest quality possible, but no additional gain. The result may be similar to using Wiimode on WiiU. While on Wii mode, many users describe a sharper picture and richer colors than the original Wii, a result of the digital output.
Perhaps (but only perhaps) there is a decrease in lag in LCD TVs. With the digital signal, television can display the image directly, with less post-processing (and without upscaling). However, on the other hand, the adapter itself may bring some amount of lag.
