That doesn't really answer my question about why you would choose barbed wire over a less harmful option.
If the OP is going to the expense and trouble of having a fence put up because her neighbour won't, why do you think a barbed wire one is the way to go? A normal, less harmful fence would do the same job, so why suggest something harmful that still requires a careless, possibly neglectful owner to take further steps?
She's already proved that she won't/doesn't want to put up a fence of her own or supervise her dog.
Forcing her hand with a barbed wire fence could end up with a bleeding, blind, or dead dog.
And yes, it would be her fault for her non-action. But the dog would still be the one with ripped open wounds, gouged out eyes, or injuries that killed it. It's still punishing the dog to prove a point to the owner.
But to some extent it would also be down to the OP's actions as well.
If she chose a fence that could harm the neighbours dog, with the motive that doing so would either force her neighbour to step up and build a second fence or do nothing and have an animal take the consequences, I think it would be partly the OP's fault if the dog was hurt. When she could just chose a fence that does the job without harming an animal. As I said before, the barbed wire choice smacks of actively wanting an animal to be hurt just so you can say "I told you so" to the owner. Which is wrong, and cruel.
The OP would also be risking her own dog should it ever decide to walk near or through the hedge into the wire, put visiting animals or children to any of the gardens at risk, possibly harm wandering cats from surrounding houses, or harm whatever wildlife happens to wander though the gardens, just so she could say that this owner deserved it because she didn't restrain her own harmless, friendly, but slightly annoying dog.
Thankfully she's said she's not going to take this cruel option.