Ugh I actually just tried playing Brawl using the Wiimote + Nunchuk last week, since I wanted to try playing it on my Wii U and I didn't have a Classic Controller Pro yet (I just got one though). The D-pad, +, - and A+B are not practical for the main three functions (jump, attack, special). Which leaves A, B, Z and C to be used for them. B, C and Z are where I'm used to only shielding and throwing (i.e. used by index fingers). And additionally, that makes it so that at least one of them will be used by my left hand. If you're used to using a GameCube controller or a Classic Controller, it's really quite difficult to get used to.
Note that I have relatively small hands (less than 7" from middle fingertip to heel of the palm) so if you have large hands, some buttons should be easier to reach, and the smaller controllers may be more awkward.
I have no knowledge about how responsive the wireless options are relative to each other.
Given the redundancy in the control scheme, some issues could be ameliorated by, for example, only shielding with L and grabbing with R. You would need to get used to it, but there's nothing inherently wrong with that scheme. Particularly on controls with only digital shoulder buttons. You can also map a function to one of the redundant jump buttons on many of the controls.
Another big thing to note is that we don't know whether the Wii Classic Controllers will even be usable with the game. For example, New Super Mario Bros U supports only the GamePad, Wii Remote and Wii U Pro Controller. There doesn't seem like there should be any
technical reason why they couldn't be supported though. But from what I can tell, most games made for the Wii U specifically do not support them. But with Brawl Sakurai seemed to want to be as liberal as possible with controller options (Mario Kart Wii was also that way), so he might do it.
Anyway here's how I would rank them, assuming they're all usable (yes, I have used all of these):
GameCube wired controller > Wii U Pro Controller > Wii Classic Controller Pro > GameCube controller with adapter > Wii U GamePad > Wii Classic Controller > Wii Remote + Nunchuk > Wii Remote alone > Balance Board
Ranking given controllers that are basically guaranteed to be usable:
Wii U Pro Controller > Wii U GamePad > Wii Remote + Nunchuk > Wii Remote alone
Your choices are much clearer if the Wii Classic Controllers are not usable.
GameCube wired: (This would apply to Brawl)
Pros:
- Most comfortable to hold, pretty light
- Wires mean that interference is no issue if you have many consoles in one area
- Off-set joysticks (high on the left, low on the right)
- Most responsive
- Buttons have a satisfying feel (on a new controller)
- Joysticks have octagonal wells
- No batteries required
- I'm most used to it
Cons:
- Not available for use with Smash Bros 4
- The Z-button is more awkwardly placed than on the Wii U Pro Controller/GamePad
- The strange layout of the ABXY buttons is probably suboptimal, although I'm used to it.
- Distance between XY and B and XY and C-stick is the largest
- C-stick's nub shape is not optimal. The way it is used in Smash mostly makes this not a problem though
- Wires can get in the way, limit how far away you can be, etc. A minor issue, but should be noted
- D-Pad is too small and too far away, although this is basically irrelevant since taunting is not important
- Most of them are old and worn out. This is not inherent to the controller though (you can find new ones, I actually just got a new one for only $30 online. You have to be wary of knockoffs and you'll have to look around to find a low priced one)
Wii U Pro Controller:
Pros:
- Comfortable and light to hold
- All buttons are in easy reach (+ and - are harder, but still quite easy to reach)
- L-stick is placed high
- Buttons have a satisfying feel to them
- Built-in rechargeable battery
Cons:
- R-stick is placed high
- Joysticks have circular wells, giving less guidance. I'm not sure how much this will matter in practice.
- Only usable with Wii U games. Therefore can't be used to play Brawl. This is my biggest complaint about it. They really should be able to release an update for the Wii U's firmware that addresses this.
- (Irrelevant to Smash, but there are no analog buttons, including no analog triggers.)
If they gave it a more GameCube-inspired shape (for the grip), off-set the joysticks and enabled it for use with Wii games, it would be awesome. As it is, it's still very good. Analog buttons would be nice I suppose, but I think that ship has sailed as the GamePad lacks them as well. This shape may be more comfortable than the GameCube control for people with larger hands though.
Wii Classic Controller Pro:
Pros:
- Fairly comfortable and light to hold in itself (i.e. not including the Wii Remote)
- All important buttons are in easy reach (+ and - are a little more difficult)
- R-stick is placed low
- Joysticks have octagonal wells
- Usable with both Wii U and Wii games
Cons:
- L-stick is placed low
- Joysticks are too tall in my opinion, which makes transitioning between ABXY and the R-stick more awkward
- Buttons feel a bit cheap
- You have to do something with the Wii Remote it's connected to, though in most situations this will only be a minor inconvenience
- Requires you to provide batteries
BONUS
GameCube using adapter to connect to Wii Remote:
Pros:
- All the pros and cons of the GameCube controllers' button configuration and comfort. Overall a strong pro point
- Seems to be just as responsive as a Classic Controller
- Adapter has a turbo feature
- Long cord gives you more options with putting the Wii Remote somewhere out of the way.
Cons:
- It seems to have some inconsistency. When I initially plug it in on the Wii U home menu, it sometimes registers inputs that I am not making. However, once you get it working, it seems to work consistently.
- It is treated as equivalent to a Classic Controller. Z is mapped to ZR, and you will not have access to ZL, if you wanted it for something.
- Start requires a double press to get + (which is pause in Brawl at least) and a long press to get Home
- Turbo feature means this won't be tournament legal. If you're playing casually, that's not a problem though. Perhaps in the future they'll release a non-turbo version.
- Requires adapter (costs ~ $18)
- Requires you to provide batteries, of course
I haven't used it for a long period, so it remains to be seen how reliable it is. If after more testing, the phantom inputs seem like a serious problem, I will probably rank this below the Wii Classic Controller.
Wii U GamePad:
Pros:
- All important buttons are in easy reach. (+ and - are not super easy)
- L-stick is placed high
- Buttons have a satisfying feel
- You will have access to any touchscreen functionality (Sakurai has said the touchscreen will not give a player any advantage; this doesn't mean it won't be used for extras like taking pictures, menu navigation, etc.)
- Built-in rechargeable battery
Cons:
- R-stick is placed high
- Distance between ABXY and R-stick is a bit large, but not as large as on the GameCube controller
- the R/L and ZR/ZL trigger buttons are a bit too far apart
- Joysticks have circular wells
- You can only use one, so in a local multiplayer game, you'll need other controls.
- Heaviest option. In playing non-motion control games on the Wii U, I have found that it's not actually tiring to hold (it can get tiring if you're using the gyroscope for a long time)
Since I know it looks like it could be uncomfortable, I will also note that it's surprisingly comfortable to hold, so I wouldn't mark it down for that. Not as comfortable as the above options though, so I wouldn't mark it up either.
Wii Classic Controller:
Pros:
- Very light
- R-stick is placed low
- Joysticks have octagonal wells
- Most important buttons are in easy reach
Cons:
- L-stick is placed low
- ZL and ZR are very awkwardly placed. I almost certainly would remap grab (taking one of the redundant shield buttons, although you could take a jump button if you wanted)
- Joysticks are too tall IMO, which makes transitioning between ABXY and the R-stick more awkward
- Buttons feel a bit cheap
- You have to do something with the Wii Remote it's connected to, though in most situations this will only be a minor inconvenience
- Requires you to provide batteries
Note: I haven't played Smash with this controller. However, ZL and ZR were awkward enough to use in Xenoblade Chronicles, and I didn't even need them very often in that game, so I'm quite sure they would be unworkable for Smash.
Wii Remote + Nunchuk:
Pros:
- Joystick is well-placed and has a octagonal well
- Ability to separate your left and right hand may be preferred by some (I will note that it does enable you to scratch yourself without interrupting play if it's just a slight itch on your nose or the like)
- Pretty comfortable to hold (the asymmetrical weights slightly bother me though)
- Wii Remote buttons have a satisfying feel
- Control scheme is completely ambidextrous
Cons:
- While Shake Smash offers an ok substitute for the lack of a second joystick, it is not as precise and may sometimes register when you don't want it to
- The C button is a little too far from the Z button
- A+B and 1+2 combination inputs will not always register properly
- D-Pad inputs are not easy to reach and do not always register properly.
- The 1, 2, + and - buttons are all difficult to reach
- There are not enough convenient buttons to cover all the important functions (attack, special, jump, shield, grab) without using tap-jump. I consider the convenient buttons to be A, B, C and Z
- You have to get used to using your index fingers for functions you'd use your thumb for with other controls (you can get used to this however)
- Assuming you don't use tap-jump, you will have to use your left hand for functions you wouldn't use it for on other controls (you can get used to this however)
- Nunchuk trigger buttons feel cheap
- Requires you to provide batteries
I do NOT like this control. The only reason it's above the Wii Remote alone is that you have the joystick and you don't HAVE to use tap-jump.
Wii Remote alone:
Pros:
- You will never accidentally enter a run, since you must double tap to run.
- Use of digital directional input can make some moves easier. F-tilts in particular are easier because you won't accidentally enter a run. Smashes and tilts have more distinct inputs (IMO).
- May be a less intimidating control scheme for some beginning players. I doubt this applies to anyone reading this. This is only a positive if they're unfamiliar with more complicated controllers, and if they make the mistake of thinking less buttons = simpler and easier to use. The extra effort to learn the positions of the additional buttons on other controls will only be a problem for a short period and after that the controls will be much easier than the Wii Remote offers.
Cons:
- No joystick means you're limited to 8 directions, and diagonals are not as easily registered. This is relevant for some moves
- A+B and 1+2 will sometimes not register properly
- You are basically required to use tap-jump. This makes up-tilts impossible to do from resting position. The D-pad will sometimes register a jump when you did not intend one.
- The + and - buttons are difficult to reach
- B is awkward and for many people will actually be activated with the back of the middle finger (at least, it would be for me)
- Not the most comfortable controller
So there you go. That's a comprehensive run down of the potential control options for SSB Wii U.
I would say definitely get a Wii U Pro Controller or a Wii Classic Controller Pro. If you wanna give it a shot, the GameCube adapter might be a good choice.