Just to clear this up. You can't play Gamecube games like Super Mario sunshine and Luigi's Mansion with digital shoulder buttons. So this most likely will not play Gamecube games.
Personally, I don't like the handles. They restrict the way you can hold the controller and make your hands sweaty if it's warm in the room. With the old Classic Controller you can hold it any way you want with any sized hands, plus the cord on the bottom is weird, but it actually makes more sense. The rows of shoulder buttons on the PRO work better though.
For me the Classic Controller is for SNES games and SNES games only, that's what it does and that's what it's good for. For N64 games I use a GC controller.
"Now, a fun game should always be easy to understand - you should be able to take one look at it and know what you have to do straight away. It should be so well constructed that you can tell at a glance what your goal is and, even if you don’t succeed, you’ll blame yourself rather than the game. Moreover, the people standing around watching the game have also got to be able to enjoy it." - Shiggy
A Koopa's Revenge II gameplay video