The C-stick is not any faster than using the control stick however it is more useful to do aerials with as it helps you control your momentum better. You can Dair with the C-stick without fastfalling, you can Uair without worrying about jumping, and you can Fair while moving forward. On the ground the C-stick is used for smashes, but its no faster than using the Control stick(although I assume you charge a little by mistake when you use the Control stick causing a little more damage) The C-stick is also better for what I refer to as "SHFFL spam" where you spam SHFFL'd Bairs with Kirby in place. This is more difficult to do with the Control Stick as you will usually end up moving backwards while doing it.
Other little odd things you can do with the C-Stick, ummmmmm, if you hold it as you put your shield up it will allow you to roll on the first possible frame. Its obviously useful for Smash DI and SDI techs(hard to do btw) Also, while completely unrelated to Kirby, if your playing as the spacies and you hang on the ledge and hit back on the C-stick and Forward B on the control stick, you can fantasm from the ledge, to the ledge(you may have seen Zhu doing it in his sig) Ummm the C-stick can be used to drop from the ledge without worrying about fastfalling, although if you hold it too long you'll just end up attacking. There's a C-Stick guide floating around the Melee forums, if I find it I'll post it for you, but for right now thats all I got.