I have to vote for high tensil fencing too. I have it around both my pastures with solar fencers on two of them and a electric fencer on the front fence. The sheep learn early, as young lambs, that the wire will "poke" them when they get close enough to sniff it and they seldom challenge it. The "poke" isn't really that painful for the sheep, they just jump back unlike my border collie who insists on slipping under the fence and getting zapped on the tail and then yelps all the way to the house. Seems she considers it a challenge since she chooses to do it for no apparent reason. The fence on the big pasture where the ewes summer wasn't on for most of the grazing season and I did not have any escapes. We don't have a problem with coyotes in this area yet, if we did I would need to rethink the wire because I think it is easy for them to get thru it.
Disadvantages, you HAVE to keep the grass and weeds out from under the fence. I do this by spraying with roundup before the sheep go in that pasture in the spring and some trimming with a weed whip of I have to. You have to be deligent about checking the fence, I do about every three days when sheep are in the pasture, but you should be checking on your animals that often anyway. Also the deer can't see the fencing during the winter and I have to replace some insulators every spring where they run into or try to jump over and miss. I've not found a deer tangled in the fencing, it does have "give" when an animal hits it and the insulators holding the wire pop out if hit very hard.
Advantages, the biggest is cost. It is much more economical to use high tensil wire. I cost it out for a section of pasture I need to do this spring, three acres with a cross fence, HT = 530.00 verses woven = 877.00, this is just for supplies, your labor would be more with the woven too. These costs are as of last fall, I looked at a roll of woven wire fence a couple weeks ago and I think the price was half again as much. Your post holes are further apart, less posts, and the wire is much cheaper, you do however need to be careful about installation and be sure your end and corner posts are set securely. If you ever need to move the fence or take it down it will be much easier with the HT. HT is easier to install in hilly locations. Stretching woven wire takes a bit of skill where HT is stretched after it is strung, one wire at a time. Replacing a post if one should get broken or split is easier too.
The fella who shears for me has 200-400 head of sheep on pasture and has used HT on his farm, switching from woven. He said his lane between the fields he has different ewes and rams in is HT and he has not yet had a ram go through the fence. Always possible if the electric goes off or it get grounded or if you have a REALLY tough ram (if he could do that would you want him on your place anyway?) but highly unlikely. Hope this helps.