I had to board, for a few years, over 20 years ago. Both barns were converted dairy barns so had cement floors.
One of my horses stocks up on cement (no mats back in those old country days) and they had to bed him really deep. 6" - 8" at least.
I prefer to have dirt floors with several inches of crush, then grid mats on top of that so at least some of the urine has a place to go to besides splattering up between solid mats and hitting me in the legs
My barn is only 24 X 40, and I do have solid mats down in the areas that are open and walkable. As someone else mentioned, they sure do keep the dust down. Ammonia:
As has already been mentioned, the ammonia from the urine can cause respiratory problems --- especially in the high heat & humidity many of us are experiencing and the air is "hanging heavy".
Humans with breathing problems can hardly deal with it, plus it's just plain unsanitary to leave the urine-soaked shavings go without being cleaned for too long.
I pick manure every day and have always deep-cleaned the stalls once a week. This summer has been that rule-breaker. I have two horses that "p** a river" and darn them, they wait until as soon as they come in their stalls at night. I have been deep-cleaning their stalls 2 -3 times a week. The other two get a sort-of-deep-clean twice a week.
Pouring cement is very expensive, so it will probably be a matter of what you can afford and what your personal preference will end up being
If I only had money for cement floors or ventilation, I would spend it on ventilation. Meaning those huge fans that suck the hot air out and are either put into the walls at each end of the barn or in the ceilings. My ex-SIL had them put in the ceiling of her barn and she loves them.