We don't like HT here. Have had too many coyotes run cattle through it, have had 2 calves get hind legs caught as they try to go through and hung up and died. Take deer out of it that have gotten caught trying to jump over. Constantly having to check the electric on it cuz if it isn't hot, a cow can just push her way through it for the "better grass" on the other side. It will not stop any smaller predator like coyotes or dogs. We also have sheep. Some will learn to respect it, but we have white dall sheep.....and have had barbadoes black belly and mouflons. Semi-wild, no respect for anything they can put their head through or under and push. Have friends with goats that will respect a 3 wire electric fence until they are running from coyotes....then it won't stop them.
Anything we re-fence is woven wire. I think it is high tensile woven wire, but I don't do the fencing. It is a good barrier for dogs and coyotes, put close to the ground; nothing goes through it. Run a strand of barbed wire on the top so the cows don't try to constantly reach over and push it down over time.
I think that fencing needs to be appropriate to the area, and what you are running. Deer here are such a nusiance and they tear up more fences in the woods that are barbed wire and high tensile. I've watched deer that will do all they can to go under or through a fence and then jump as a last result. Doesn't take long for a regular deer run to make a small hole between 2 strands as it gets stretched a bit or 2 wires get wound up on each other. Then a calf finds it, and they are getting out.
But it is personal preference. And we like the added versatility that a good woven wire fence gives us. Mostly keeps everything in, including the places we have free ranging chickens.