Composite video is a
composite of all the video signals into 1 yellow cable.
Component video splits each video
component into 3 cables: red, green & blue.
Both have left & right audio in their own white & red cables.
Composite is much more common, and is therefore better if you plan to take your cable with you (on vacation to plug into the hotel TV, etc.)
Component video is meant to provide a better quality picture, but since the video source is a compressed video from an iPod or iPhone, I don't know if the component video would look any better than the composite video.
(I have both connections on my TV at home - I literally stood in the Apple store with the component cable box in my left hand, the composite box in my right hand, and me doing my best to not block any aisles trying to decide which to get. I bought the composite (yellow, white, red) cable, and was glad I did when I plugged it into a hotel TV and watched a movie on TV with it.)