This fence is known by a lot of names: box wire, woven wire, non-climb, etc. We will use the term woven wire to describe any fence that has vertical and horizontal wires connected to form a grid. These grids can be many different sizes depending on the distance between the wires.
Woven wire’s advantage over all other fences is its security; woven wire fences are specifically designed to keep animals in or out. A tight grid of wires nailed securely on sturdy posts can keep something as small as a rabbit out and or keep an animal as big as a horse in. The only way animals can get through is if the woven wire fence is actually broken.
If security is your highest priority then this should clearly be your fence of choice.