I used to use woven wire to hold hogs, and have a woven wire around my horse lot, and garden. I'd like to have part of the cattle pasture fenced in with it, but barbed is cheaper and easier for be to put up, especially if I'm doing it by myself.
We've got a few areas where we've used it but like you mention barbed (and electric) is so much easier if you have to do it by yourself. Of course I don't have one of the woven wire roller frames that fit on a 3 point hitch so I just roll it on the ground then tension with a bar run through it at the end. I'd definitely get one of the 3 point roller/tensioners if I was going to do a lot of it.
I think the best all around sheep/goat fence would be the class 3 no-climb horse fencing with the smaller holes. Goats will get their head stuck in the regular woven wire....heads can be shoved through but the horns stop them from coming back out. It's expensive and a headache to install.
The majority of what we have is barbed with a strand of electric below the bottom and between the first and second run of barbed.....it works really well for turning coyotes....as long as it isn't grounded/wrapped on the barb wire. Have replaced about 1/2 of the low tensile electric with high tensile and I'm VERY happy with it. Will be starting on replacing the rest now that hunting season ended.