GameCube:GameCube vs Wii
The GameCube outputs much better quality video than the original Wii systems, however some later model Wii's output at a quality very close to the GameCube.
For technical information and pictures on GameCube vs. Wii output, please see this thread (and thanks to Sixfortyfive and Artemio for putting all that work in!): http://shmups.system11.org/viewtopic.php?f=6&t=51789
According to this page, the Wii without Gamecube ports is the RVK model and they are pretty much the same as the RVL-CPU-40 and 60, which do have Gamecube ports and play GC games: http://www.bitbuilt.net/forums/index.php?threads/shanks-wii-super-thread.66/
Someone recently did a great comparison of Gamecube games played on the GC, Wii and softmodded Wii U. If you'd like more details and picture comparisons check it out: https://socksfelloff.wordpress.com/2015/03/15/gamecube-vs-nintendont-vs-wii/
If you only play one or two GameCube games, than it's probably not worth the time/effort/money hunting down a later edition Wii. If you're a big GameCube fan, it's definitely worth either getting the official GC component cables, or getting the new GCVideo mod. Many more examples of GC vs Wii differences are available in the first link, but here's some basic GC via original Wii comparisons, both with the official component cables.