Overall, the cube and the classic are almost equal, but I've already found a couple of points that swing the balance in favor of the classic:
1. Shielding. Shielding in Brawl is digital, but the cube triggers are analog, so you have to push them all the way down to register. This will give a slight delay to shielding that you don't get with any of the other control schemes. The analog triggers mean that L and R are basically useless on a cube controller if you want quick and accurate responses. You could map shield to X or Y, but then you are running your fight entirely with your thumbs, and the right thumb already has to manage jump, attack, and smash.
With the classic controller, L and R give an instant response on shielding, so you can use them just fine, or map them to another function. Either way, you can use your thumbs and your two index fingers to share the load on function management. ZL and ZR are awkwardly placed. You won't be using them, but they aren't needed anyway. All smash functions can be accounted for without using those buttons.
2. Dedicated grab button. I know cube has the Z button, but I find that awkwardly placed. With classic, you can have jump, attack, smash, and grab all on face buttons if you want. I know you can shield+attack to grab, but having a dedicated button is probably a good idea for quick tether recoveries, quickly tossing items or spent item guns, etc. Besides, maybe one in 100 times I've tried shield+attack to tether and wound up air dodging off the stage instead. It seems like grabbing is a bit more useful in Brawl than previous iterations, so I feel better having a dedicated and easily accessible grab button.
The comfort level of a cube is a bit higher than an unmodded classic, but the Nyko grip attachment solves that problem nicely.
Again, the cube controller is an ok way to play, but I think there are still a few minor flaws that keep it below the classic controller. I have a sneaking suspicion that most of the anti-classic comments are coming from either those that never bought one and just want to put it down because they can't use it, or from stubborn Melee vets that are unable to learn a new control style and so will of course suck in competition whenever using a Wii control setup. On that note, I noticed that not nearly as many people insisted on trying to play Melee with an N64 controller, but oh well.