Barbed wire is not a good fence for goats. At all. Not added to another fence, not by it's self. I would completely not even consider using that. It's no good for them. It will not keep them in. Goats will try to get out of anything. So adding to the fact they will escape, you will have many injuries from them climbing, digging, jumping, or crawling out.
The wire, electic or not, may work. I don't really know. I have shyed away from the stuff because I also have horses. And it works like a cheeser grader if they run though it because of low visibility. Around here the best way to keep them in is 2"x4" fencing. It has to be sturdy, lots of posts and tight, an electric wire on top helps, and even better would be another electric strand about a foot off the ground on the inside.
I've had goats for years. I have yet to see a fence they will not escape eventually. They will loosen nails, dig holes, climb anything. The little stinkers. lol. We have some 6' high chainlink they can still get out. We had to pound iron bars into the ground every foot to keep them from digging out.
But my 2"x4" holds out the best for sure. The only problems we have is if they lean on it too much and bend it down, or if they loosen some nails and escape through a hole. The first was easily fixed with adding some electric. And the other is just basic fence checking.
It will keep predators out, and you can even keep chickens, rabbits, pigs, horses and dogs in. Just about anything. Love mine.
Oh I forgot to mention hog panels. They work too. Good for being able to move around fences, or for buck pens. But you have to make sure the ground is flat or again they will dig out. They can't climb over though or bend it. So it works great as well.
ETA: My goats hate rain. As with any animal you need to provide shelter.
