So now that brawl allows you to map the c-stick to other attacks, it might be a good idea to have a discussion about the advantages different mappings can have for pika so people can decide what works best for them.
So, this is my understanding so far. I might have errors so feel free to make any corrections.
So I think there's essentially three useful mappings, the standard one is
Smash - Smash lets you smash in any direction when you're standing still (dash attack if you're running) and do aerials while you're in the air. IMO, now that you can change the c-stick this seems like the least useful one. C-stick aerials are certainly cool because it allows you to DI (or not DI) the entire time rather then have to input the aerial direction then DI or worry about accidently DIing with the aerial direction you push. However, I find that smashing with the c-stick is just as easy without it, and there's nothing the the c-stick provides to smashing that you can't do the regular way given enough practice (plus its easier to stall a smash or charge it the regular way)
Attack - Attack lets you do the tilt attacks in their respective direction, as well as aerials. I already went over the importance of aerials for the c-stick in the smash. Tilts imo opinion are harder to pull off for all their applications then a smash, especially a side tilt. But more importantly, tilts allow you freedom of movement that a smash attack does not. For instance, I can move sideways and do an up or down tilt or crouch and spam utilts/side tilts, something that becomes impractical or impossible without the c-stick mapped to attack.
This was never relevant to smash attacks because I could hold pikachus movement in a direction/make him crouch, do the smash before his movement,crouching animation would end, and then have my finger back in the position he was headed/facing before the smash attack would even finish.
Special - This might be one that's only worth it for pikachu. He can do all his directional b-attacks and through voodoo magic his neutral (I can explain how, but its really not worth it). His side b doesn't have a great benefit with the c-stick, although no problems really either. You can only charge it if you press z while you use it. His down-b has one useful application with the c-stick. If you thunder diagnolly in the direction you want to fall, your momentum will change instantaneously as soon as you hit the thunder. Without the c-stick, you generally had to change your momentum and then thunder afterwards. Not huge, but still pretty helpful. [There's also a weird glitch where if you do change your direction backwards with the analog stick first, and then thunder, your momentum will change back to its original momentum.]
But the most useful aspect of changing his c-stick to special is for his quick attack. By doing so, you allow yourself an incredibly large increase in mobility with pikachu's QAC. It's hard to describe how much this increases your mobility without practicing and trying it for yourself, but it does take practice to pull out the potential of QAing using the c-stick. Here's a basic overview anyway. Since pikachu's normal QA requires that you push up on the analog stick and then input the direction you want to go, moving about becomes a slightly more arduous task, let alone doing a second quick attack where you would have to once again, push up on the analog stick and input the direction again. The c-stick allows you to pull off a QA and already have the direction you want to go instantaneously, making it incredibly easier to pull of multiple QA's (with QAC) that may have only been possible before with beyond human reflexes. Another useful tidbit, the standard QA with the C-stick is an short upwards QA, unless you're holding the the upwards direction. This is also helpful since pulling off short QA's in the heat of battle are difficult to do, and now doing a short QA up after a having previously done a QA is also a great deal easier.