Wow, what seems like such a simple question doesn't have such a simple answer. The most simple answer is, "it depends".
HorseMom is right that the closed-end shafts are marathon shafts, usually only used for CDEs and the like. They require a tug that can be opened to fit through the looped end. We just had to get new tugs, because our open tugs wouldn't "open" for our new marathon vehicle shafts. As far as what matters for showing, (correct me if I am wrong) it doesn't matter what shafts are used for CDEs, but some will give more advantages, just like HorseMom said.
Otherwise, for Pleasure Shows, the shape of the shafts depends more on the style of the traditional vehicle. Some very curved shafts are called Gig shafts, because they are generally used on gigs. Usually, you would use French or Tilbury tugs with Gig shafts. Some vehicles have Double Bend shafts, like mine in the avatar, that basically allow for the design of the vehicle. In my case, it allows for easier entry. There are also Bent Heel shafts, which have one 90 degree bend in the back, again for the vehicle design.
How does that muddy the waters!
Is there something specific you would like to know?