In reply to Trangia:
To state the obvious - fences are there for a reason - largely to prevent stock wandering into places they shouldn’t be. Most wire (pig netting) and pole fences are actually rather flimsy and a herd of cattle would make short work of them. The point of putting barbed wire as the top strand (and sometimes the bottom strand) is to prevent cattle from destroying the fence as the barbs are painful when a cow tries to push the fence down or climb over it. They learn this and respect the fence.
Now to the point of your post, do you want to discourage large stock from accessing the fenced off path you are walking along, if so then barbed wire is by far the most cost effective and permanent method of doing so - electric fences are temporary (and as engineered at present, rather flimsy), they also require constant attention (battery changes), carry the risk of shock to people, and they’re more expensive over time.
If you are getting snagged when just walking along as opposed to climbing over a fence it’s probably worth having a word with the owner with a view to getting the problem looked at, as no one likes damage to their kit. Although most fences you come across won’t be owned by the NT and you probably don’t know the landowner, so reporting it might not be particularly straightforward.
Otherwise it’s one of life’s minor hazards, that we encounter and have to negotiate with care and attention.