My personal list of Pros and Cons for switching from CG to Classic Controller:
PROs (from most important to least important)
Y button right above B button, allows Jump Canceled B Specials, like OoS FJPs, without Tap Jump.
Two Z buttons means an extra button... useful for ATs.
Right Analog "C-Stick" closer to the face buttons for quicker use, and more comfortable too.
No chord to the Wii means people wont trip over the cable and almost drop your Wii.
No chord to the Wii means it wont add to the cables braiding as people pass around the controllers.
CONs (from most important to least important)
So small! No matter how used to it you are, it's still not as comfortable as CG (unless you do as Kig says).
Analogs so low that your thumbs might need a week or two to adjust to "where is up". *
New layout and positioning of buttons will make you suck for a few days as you get used to it.
Plugging and unplugging GC when passing around controllers for turns becomes a hassle.
You have to put a Wiimote in your pocket or find some other place for it.
* Your left thumb sort of turns sideways to reach the lower Left Analog Stick and the motion it used to make to move "up" now results in "up-right" diagonal. The right thumb is already used to this low position, though.
I must say, though the entire list may be incomplete, the CONs are mostly things you can overcome by "getting used to it".