My advice is that if there is fencefighting, it sucks. I've got that problem with my neighbor dog, and I hate it. My dogs are not naturally fence aggressive, they wouldn't really care about any dog on the other side of the fence (wood privacy fence). But they don't react well to the death threats. It used to be only Tully who responded, but Pirate is such a boy, he got involved too. And with Tully incapacitated and then gone, Tess decided she had to back Pirate up.
I've had injuries from my dogs charging the fence (Tully lacerated a pad bad enough to take her to the vet once), as well as the major incident where the neighbor dogs mauled mine, of course. And I worry about the behavior my dogs are learning.
The inner fence is probably the best option. A hotwire will also work, and is relatively inexpensive, but I think it's illegal here.