At one time here in Va you had to build 8 strand barbed wire for it to be a LEGAL fence. Several counties have stipulations on what constitutes a legal fence.
As I said earlier. it is what you want personally, and what is prevalent in the area. I would think that 10 strand barbed wire could keep in most anything, but the chickens maybe...... but again, it is what you prefer, and what is considered legal in places that have regulations. Interior fences are a whole different story. We had several BB barbados that got out of some barbed wire/high tensile combination and after running the neighborhood and being unable to catch them, wound up shooting them.
Another thing to consider is where you live and the traffic if near a road, and the neighbors.....besides any legal restrictions. All the original poster asked for was opinions on who liked what, and lots of us expressed that.
I can climb a woven wire fence in an emergency next to a post. I could never climb a barbed wire fence that was 6-10 strands without getting hurt.... I am not that agile anymore; and I cannot go through it if it is real tight either, even if it is only 5 strands. There might not be a gate close to where you might need to go over in some sort of an emergency.