QH's are probably the most common nowadays in professional ranching. Cattle camps and range riders tend to use more of a variety at least where I live(Montana) - my landlord's herd of cow horses ranges from Welsh/Perchs, Fjords, QH's, Arabs, Quarabs, Draft X's, to mustangs. I think QH's are probably one of the easiest breeds to get, as well as that they typically have a good disposition for working cattle, so that's why they're pretty popular among cowboys. There's really no "one breed" that does it all though.
Big horses are more useful for roping and working cows, but I've seen that a lot of riders tend to prefer the "smoothest and surest" horse when it comes to range riding. Whether that be the TB, QH, mustang, or grade, it doesn't really matter.
"The art of riding is hard to find and easily lost."