When all we had here was woven wire or single barbed wire and smooth wire, here called pony wire, our then vet told us, smooth wire caused the worst injuries, barbed wire not as bad.
His idea is that barbed wire is respected by horses and if they hit it, they notice it more.
Smooth wire, horses don’t respect it, lean on it or push on it, barely believing it is a fence.
When they run thru it, it slices before they know it is doing it and so doesn’t stop them, while barbed wire stings and they pull up.
I know that a neighbor made a whole large trap of pony wire, thinking his broodmares and foals would be safer than with barbed wire, but had injuries in it.
We have had barbed wire here for over 100 years, with all kinds of horses and have very, very rarely had a horse injured on it and then not very badly.
I have seen some really bad injuries at the vet from barbed wire, so have I from board fences too.
I think that horses and injuries are part of having horses, they are injury prone.
Some common sense in fencing, the right horses under the right management for the fences you have and a big dollop of luck is what keeps horses as safe as we can manage.