I'm just noticing that every stream I see on the leaderboard uses the Wii instead of the actual Gamecube... why is that? Is there any benefit to it?

Reason being I already have my GC set up and I'm ready to run.

Extensive testing hasn't been done to determine exact time differences, but you mainly see Wiis used because they're easier to region-free and load practice codes on than GCN. If you've got your Gamecube set up I'd just stick with Gamecube for now.