Doing a raw Dolphin video comparison to the Wii version doesn't really accurately mimic an actual Wii though. The brightness setting of REmake in Dolphin is broken.
It's broken to the respect that I believe it may actually be stuck on max brightness. If you go into the in-game brightness slider changing it causes no change. On top of that, people already know and have noticed that the visuals look off. They look overly brightened and dull.
I really do recommend if you want to do a side by side comparison, at least use SweetFx to try and get the visuals close to how they actually looked on Gamecube/Wii.
Here are some examples of how the game is actually displayed on real hardware
Anything else isn't really doing service as a proper comparison.
As I showed on a previous page, I have a SweetFx profile if you want to use it that at least closely emulates the proper contrast levels of the visuals on Gamecube.
Here's the comparison I made.
Vanilla remake, SweetFx'd, Actual hardware
Here's the SweetFx download