We have barbed wire. 40 acres east of our house. 75 west of our house. All barbed wire. BUT. we run cattle too and I can tell you what cows do with horsewire - they walk right through a five strand fence like deer will do.
The only strip that isn't barbed wire is the stretch of fence directly behind the house and it is horse wire, with a hot wire ran down the same stretch to... dissuade... persistent heifers. (Swimming pool floaties, a fence placed to darn close to the pool, pool floaties, and a windy hill equal spending a fortune in pool floaties every year. I made him tear out the barbed wire and put in horse wire to save the floaties)
SO FAR I haven't had any barbed wire injuries on our horses. I've seen cuts and tears on them from brush, briers, and stobs on trees though. BUT. As others have said - the size of the acreage makes a difference. If my horses spook, they have a long way to run before they hit fence. If they squabble, they don't do it right against the fence, they like to be in the open where they have room to maneuver.
However. I'd say if you don't have to use it, don't.
We have no choice really - can't run hot wire around the whole perimeter of both sides of our property - deer bust through it, sticks fall down out of trees and ground it out. We tried, fought it for a year in the creek bottom west of us, and it was a daily patch job. Finally gave up. Cows don't give a fig about horse wire, and steel pipe fencing won't get it done either - the ground is too wet, water table is just three feet below the surface in the low areas of our land.
"We are here to laugh at the odds and live our lives so well that death will tremble to take us."