A slightly different perspective...
I bed a Jersey milk cow.
I understand that cows bedded on straw are much less likely to develop mastitis (infection/inflammation of mammary tissue from bacteria coming up from the teats into the bag) than cows bedded on straw.
Apparently the straw is a less friendly medium for bacterial growth than shavings are.
My cow is not terribly susceptible to mastitis (some cows are, some aren't so much).
The cow's bed is shavings on the bottom, to absorb pee better, and straw on top.
Straw can be much less expensive than shavings, depending where you are; where I am it costs around $20-$25/stall to bed in shavings, $6 to bed with straw. Waste with straw is about twice as much as shavings, though.
I much prefer pellets or shavings over straw; much easier to clean and dispose of, especially for teenage working students. I will bed with straw over the winter though; I swear it keeps ambient temp in the stalls a little higher, and it does give the horses something to do during the longer nights! Then, I switch back to pellets during the summer months.
The straw never would soak up all of my horses urine and would end up being wet and soaking wet. My blankets would also smell and be soaked in urine from him laying down. I use shavings now because it was just gross and he stays dry.
Whether you choose shavings or straw (or pellets or alternative paper based beddings) will depend for the most part on what you are used to, what's prevalent in the area you're in, and what the disposal options are..
I consider straw to be more sustainable, as it takes no time compared to trees to replenish what's been harvested with a new crop.
It's no harder (indeed, straw is lighter) than other types of bedding to handle, but it takes a knack to clean a straw stall correctly; if you don't know how, find someone who does so you can learn before you decide to use it. If you aren't cleaning correctly, or you are using inadequate amounts of straw you might decide you don't like it, but IME, there is nothing more pleasant and easy to use.
With a nicely banked shavings stall requiring 8-10 bags of shavings, it can be really pricey ($60-80 or even more) to bed down a stall; depending on how much a bale of straw is and how big it is, only 2-3 are needed; often this will cost only $10-15. I find straw is much more economical to use, especially because our disposal is free.
On the upside for straw, in many areas (including ours) mushroom farmers will dispose of your manure pile at no cost. Most who use shavings have to rent a dumpster and pay a hauler to take it away, which can be very expensive.
I found that straw was rather easy to clean. It does take a knack. The stall needs to be bedded pretty deeply for it to work easiest. You need to use a real pitchfork, not a fork like you use for sawdust, to pick up the big piles, then move all the other straw out of the way with the pitchfork - the little turds should fall to the floor and you will find all the wet spots. Then you use the sawdust muck fork to pick up the turds and wet straw. It is not as absorbent as shavings, but I find if you have dirt floors that are properly leveled, it is easy to use as long as the seal has some time to breathe. It is much cheaper than shavings in my area - wheat straw is the best and is $3 or $4 per bale to bed a 10X10 stall (it only takes one bale) vs. $5 per bale using two bales per stall. I found I took out about 1/4 bale at the most for straw, but nearly 1/2 bale for shavings. Straw is much bulkier so it looks like you are using more than you actually are.
If I had mats, I would ideally use straw over pellets or super fine shavings to soak up the urine. I like how cushy it was, and how clean and shiny each horse came out - minus the poop smears of course. I never had a horse really eat it, though they may take a nibble or two. Straw really isn't that appetizing!
I agree with it comes down to personal preference. I can't account for cost differences as a factor (if it is one). Shaving is the popular bedding choice with hunter/jumper barns in my area. After that it seems to be pellets, then straw in terms of popularity.
I think there's a definite geographic preference. In VA/MD, I only knew of two barns that used straw- one was my friend's (whose grandparents are racehorse owners & breeders in va & fl) and the other, a VA foxhunt master's barn. In KY, IME 90% of the big breeding/racehorse barns use straw. The only ones I remember that werent were sport horses.
Personally, shavings over straw b/c straw makes me itchy & hate mucking it out. But I only like certain types of shavings.
And the wise, Jack Daniels drinking, slow-truck-driving, veteran TB handler who took "no shit from no hoss Miss L, y'hear," said: "She aint wrapped too tight."
We used straw exclusively at Sandron for many years. Old horsemen will tell you it puts a beautiful coat on them as the oils tend to polish the coats. Whatever the reason, I agree. We never had an allergy problem, ever. I think it us WAY cleaner than shavings/ sawdust and easier to clean in number of forkfuls removed (you can stack piles into one BIG forkful), and much more cushiony than shavings. But, it must be on clay or gravel dust stalls, or some other base that drains. Straw is designed to have urine go through it, not much absorption. So, very slippery on mats, and urine pools. It is also hard, as mentioned, to find consistent quality straw year round. You need to add 1/2-1 bale a day.
I would bed on straw in a NY minute if I could.
I have bedded horses on both straw and shavings. I prefer straw. My horse gets bedsores from lying down on mats and shavings, I never recall that happening with straw. I think my boarding barn probably doesn't use enough shavings. I also prefer mucking straw over sawdust. I learned to much straw as a kid and then never mucked sawdust until I was an adult, so maybe that's why. Straw does not take longer to muck if you have good technique and I feel like I waste less straw when sorting it.