While there are many 'pros' to underground fencing, one of the biggest 'cons' with underground or wireless fences is that although it offers some way to keep your dog in your yard, the invisible fence does not offer any protection to your dog from predators ... including people who steal or do harm to dogs.  The numbers of incidences of dog-napping are steadily increasing in the Central VA area.  People steal dogs left outside unattended and sell them on craigslist or at flea markets, sell them as bait dogs, sell them to research labs to be used for testing ... anything to make a buck.  And if there are coyotes or other dogs running loose in your area, your dog does not have any protection against them with an underground fence.  Your direct supervision and your ability to remove them from a dangerous situation is their only protection.

Additionally, there are liability issues that owners may face.  If someone’s pet or their child wanders into your yard and is injured (or worse) by your pet, the consequences are devastating.  While similar issues may happen in a yard with a physical fence, it is less likely that others will just ‘wander into’ a fenced area. 
 
http://dogs.thefuntimesguide.com/2006/08/invisible_fences.php

Downsides To Invisible Fences…

     If there is a power failure, your invisible fence becomes useless during that time. Therefore, if you live in an area that experiences frequent storms & power outages, you may want to reconsider installing an invisible fence.

     Under the right conditions, a panicked dog could run through the boundary, then be hesitant to come back through the barrier.

     An invisible fence may keep your dog IN the yard, but it doesn’t keep other dogs or wild animals OUT. So, there’s always a chance that your dog could be attacked or get in a fight with another dog or animal inside the boundaries of your invisible fence. (Such is why your dog should always be supervised even in a yard protected by an invisible fence.)
 
http://www.vetstreet.com/our-pet-experts/is-it-ok-to-leave-my-dog-alone-in-the-yard
 
Hanging out in a fenced yard can be a viable and safe option for some pets, but leaving a dog in a yard with an invisible fence has its own unique hazards. Though dogs usually won't leave their yards in this scenario, an invisible fence doesn't prevent other dogs from getting in the yard and attacking your dog. If you are relying on an invisible fence, be cautious: Dogs in yards with invisible fences shouldn't be left out without supervision for their own safety.

From Victoria Stillwell, one of the best-known, most-admired, positive-reinforcement trainers in the world.

https://positively.com/dog-training/methods-equipment/training-equipment/electric-fences/

An electric fence is a wireless, in-ground or ‘invisible’ fence that is installed around the perimeter of a property, creating an invisible boundary. A dog contained within the boundary of the fence wears a ‘shock’, ‘remote’ or ‘e-collar’ around his neck (and sometimes around his groin or at the base of the tail) which consists of a transmitter designed to deliver a 'static correction' should the dog stray too close to the boundary. Flags are placed at intervals around the perimeter as a visual marker.

When dogs first learn to stay within the 'fence' they inevitably receive a series of electric shocks, which supporters of these fences claim is harmless. Of course, any kind of aversive such as shock has to be relatively strong in order to be effective, and while the dog might learn to quickly associate one flag or part of the property as a no-go area, his natural curiosity will inevitably lead to subsequent shocks should he get too close to other untested areas during the ‘learning’ process.

But the likelihood of shocking the dog is only the first of many reasons why electric fences should be avoided at all costs.

Why Should You Say NO To an Electric Fence?

• Some dogs are so traumatized after just one shock experience that a fear memory is imprinted in the brain forever. While this sometimes provides enough motivation to avoid the boundary in the future, it also absolutely leads to countless other fear-based behavior issues and breaks down the human/animal bond significantly.

• Some dogs will refuse to go into their yards, while others have suffered electrical burns from the very collars fence companies claim are 'safe and humane'.

• Many dogs break through the boundary to get to something on the other side regardless of the pain they experience or because the fence has malfunctioned in some way. Many of these dogs end up getting lost, hit by cars or picked up by animal control officers (dog wardens) who regularly find these dogs wandering around the neighborhood.

• Once a dog has gone through the boundary and been shocked, he is almost guaranteed to avoid coming home because he knows it means another shock.

• Dogs contained behind electric fences tend to become more reactive and in some cases more aggressive toward strangers and even family members. A recent study found that dogs without previous aggression problems attacked family members when the system was activated.

• Similarly, delivery personnel or any guest or family member can be an unwilling victim of a dog’s pent up frustration.

• Any dog that is left outside for long periods of time is likely to develop a fence running habit, barking at cars, people or other animals as they go by, but this behavior is a lot more prevalent in dogs that have an uninterrupted view. Fence running is an unhealthy activity that exacerbates frustration, irritation and aggression and regularly becomes a fixed action pattern the dog performs in other contexts and environments, such as on a walk.

• Dogs that live within the confines of an electric fence are also at the mercy of other animals and people that may wander onto their property, and with no visible boundary, these dogs are at greater risk of being stolen. Pedigrees have a high resale value while mixed breeds are regularly stolen to be used as bait in dog fighting circles or for medical research.

  Electric fence companies would like you to believe that their 'fences' are the perfect solution for containing your dog, offering 'safety, comfort, and peace of mind,' but do not be fooled by clever marketing. While the idea of allowing your dog to experience more unsupervised 'freedom' might be an attractive option for you, the simple truth is that electric fences rely on pain to deter dogs from escaping and the risks of anxiety and aggression issues, theft and increased legal liability are too high.

  Positive Alternatives to Electric Fences
  While no fence can offer a hundred percent protection, a solid fence will do a much better job keeping your dog in and others out. If you do not have a physical fence around your property, keep your dog inside your home and take him out for regular toilet breaks and walks or invest in a solid fence around, or smaller 'dog run' within your property. It is a much safer, more humane and effective containment option than an electric fence will ever be.