I use the Gamecube. I tried the Classic for awhile, but had one issue. There are no grips for the palms of my hands. Also, having larger hands they end up going numb and cramping. If the Classic had grips (which the back seems to have an attatchment slot for) I'd use it over the Cube controllers. I'm use to the Cube, but the buttons on the Classic are much closer together, making things quicker and easier.
Another issue going from Cube to Classic is the angle of you thumb on the analog stick. If you're use to the vertical thumb from the Cube, you'll end up jump instead of running left, and crouch instead of going to the right. While not that extreme, it is more than enough to really mess someone up who used the Cube for years. If you've never used either it isn't such a problem.
The Cube has a large disadvantage with the default setup. The L and R buttons are analog in Melee, but digital in Brawl. This means you have to hold the shoulder button all the way down to bring up the shield, which is enough delay to cause you to lose. That being the biggest reason for me working with the Classic.
The WiiMote didn't work well at all. There are not enough button options, so you only have up to jump with, meaning you can't hold down when you jump to float.
The Analog attatchment to the WiiMote wasn't terrible, just odd. My biggest issue is the missing second Analog stick (the Cube's c-stick) which gets a lot of use (the Classic also has the second analog). Some of the button spacing seemed wrong to me as well, like the use of the d-pad on the WiiMote.
Something else about the Classic: The two analog sticks are close together and on the same horizontal plane. So, if you like the end of the sticks in the middle of your thumbs you'll have your fingers hitting if you jump/run to the right and use the analog to attack to the left. This just means getting use to using the tips of your fingers if you don't have ****** hands.