I don't like electric personally. I used to board in place with electric and I always worried I can be pushed against it by those horses with no manners (you don't chose other borders, you know). And even with my own, I still don't use it. But it's the cheapest one for sure.
Unfortunately, there is no such thing as the "safest" fencing. About as close as a person could likely get would be this stuff, but it's expensive as heck.
Personally, I like electric. I am currently going around our property and replacing all the old wire fencing with 1" electric tape. With that, there is nothing for them to chew up, nothing that's going to slice them open if they run through it in a panic, it's relatively cheap, and looks fairly nice. Plus, the electricity is a good deterrent for my "Houdini" animals that tend to walk through ordinary fencing.
I use 3 and 4 rail board fencing here, painted black, because I like the look of it, and rails are easy to replace...but I run a tight strand of barb wire between the top two rails in the horse paddocks. I don't recommend barbed wire for show horses as they will lose some tail hair on it.