From my own experience I would say it's the exact same, but I could easily be wrong. I've played plenty of GC games on my Wii with no problems whatsoever. New models of the Wii can't play GC games though (in North America only I believe), but I'm assuming you have one of the earlier ones.
I've played the game using both systems, and I believe they work just the same. Now on which one to play the game on, well that's your decision and it's your choice. But for my opinion, I would play it on the GameCube for Nostalgia reasons . Also if you just got the GameCube with the WW, I would put your new toy to good use.
I had a Wii and a GC together for a while and I played both of them with GC games and there wasn't a difference, except that I had to change my TV display to 4:3 for GC games on the wii because it runs on 16:9
Outside of glitches in the Wii's GC emulator or some other weird problems, it should be exactly the same; you're playing the exact same game on the same disk on different hardware. I never noticed any glitches or problems.