I used stall pellets back when I had horses and rubber mats in the stalls... urine would splash and puddle without any bedding... ick! The pellets absorbed super quick, and yes, turned to sawdust, fine with me. I liked them better than straw and shavings for that purpose. I don't think they would necessarily be bad for inside a covered run either. But you would probably want something fluffier inside a coop so chickens have a softer landing when they jump off the roosts.
I've noticed that all the local feed stores in my area use the stall pellets in the chick and duck brooders. So back when I got my first chicks I bought a bag for brooder bedding because I just thought that's what you were supposed to use. Then after 2 sets of chicks, the pellets were used up and tossed in my run mixed with shavings, and I had no complaints. 3rd set of chicks I used shavings in the brooder and it was a complete mess!! Shavings flung everywhere! and in the water and food... gross! So I bought another bag of pellets and switched out the bedding and had a lovely clean brooder until chicks went to the coop.
Sooo.... moral of the story:
I think stall pellets are absolutely best for the brooder.
Indifferent about them in the coop or run.
I think a bag of pellets won't cover near as much ground as shavings so you'd probably spend quite a bit more money to cover your space. A bale of shavings fluffs out to be A LOT! But if you have a moisture problem or an accident of spilled water, the stall pellets would soak it up in a jiffy, where shavings just get soggy and heavy after what seems like forever to soak up water and dry out again. I use shavings in the coop and run, but I do keep a bag of pellets on hand "just in case." (Of course I may be a little overzealous in all the chicken supplies I seem to hoard)