As a horse owner, I never thought to use anything other than shavings. Hay (esp. that of good quality) is a premium product and I use it to occupy them in the pen. I can certainly see how it's ability to tangle contributes to it's being ejected more completely from boxes than shavings. Hay really keeps them busy!
I do find that they evict a certain amount of the shavings on a daily basis. This is attributable to the fact that we didn't build the fronts of the boxes high enough to keep the shavings inside.
-Christian