As another poster said, the magnetic stripe on the "paper" tickets is more durable and reliable than the stripes on the plastic tickets. Also, they're coasted with something that makes them virtually indestructible. (If you have any old tickets lying around, trying ripping one in half sometime. Unless you start the rip with scissors, it's near impossible)
The only thing that can get them is if they get drenched with water. Even then, they stay intact and only curl up and won't go in the turnstiles or FastPass machines. The printing is still readable and the ticket can easily be replaced by Guest Relations.
Lastly, the WDW parks can't give you tickets on anything but the "paper" ticket stock. The ticket machines in the windows aren't designed to issue anything but the paper ones. (For economic reasons, the paper tickets come on long rolls, and each ticket is cut from the roll individually, which is why the tickets usually have a slight curve to them when you first get them)
-Rob